Exact counting of subtrees with diameter no more than d in trees: A generating function approach
Network motifs, regarded as fundamental building blocks, offer crucial insights into the structure and function of complex networks, with broad applications across disciplines including sociology, computer science, bioinformatics, chemoinformatics, and pharmaceutics. However, the identification of n...
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| Veröffentlicht in: | Information and computation Jg. 307; S. 105353 |
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01.11.2025
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| Abstract | Network motifs, regarded as fundamental building blocks, offer crucial insights into the structure and function of complex networks, with broad applications across disciplines including sociology, computer science, bioinformatics, chemoinformatics, and pharmaceutics. However, the identification of network motifs remains a significant and computationally challenging problem. Among various motifs, subtree enumeration has garnered substantial attention in recent years, particularly due to its relevance in network science and bioinformatics. For an n-vertex tree T, by introducing novel generating functions with (d+2) variables, we propose an innovative algorithm for the exact enumeration of T's subtrees rooted at fixed vertex v, where the distance between v and the farthest leaf is k=0,1,…,d, and the distance between any two leaves is no more than d. Building on this algorithm, we develop novel recursive algorithms for exact enumerating various diameter no more than d subtrees (abbreviated as DNMT-d subtrees) of T. As applications, we apply these algorithms to derive the number of DNMT-d subtrees in a full binary tree Bh with h≥2 levels, and briefly discuss the density of DNMT-d subtrees in general trees. Our research generalizes the work of Frank Ruskey on Listing and Counting Subtrees of a Tree in 1981 and makes it a special case of our study where d equals the diameter of the tree T. Moreover, the proposed O(dn2) algorithms introduce new approaches for enumerating subtrees under diameter constraints and lay the groundwork for counting diameter-constrained subgraphs (motifs) in complex networks. |
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| AbstractList | Network motifs, regarded as fundamental building blocks, offer crucial insights into the structure and function of complex networks, with broad applications across disciplines including sociology, computer science, bioinformatics, chemoinformatics, and pharmaceutics. However, the identification of network motifs remains a significant and computationally challenging problem. Among various motifs, subtree enumeration has garnered substantial attention in recent years, particularly due to its relevance in network science and bioinformatics. For an n-vertex tree T, by introducing novel generating functions with (d+2) variables, we propose an innovative algorithm for the exact enumeration of T's subtrees rooted at fixed vertex v, where the distance between v and the farthest leaf is k=0,1,…,d, and the distance between any two leaves is no more than d. Building on this algorithm, we develop novel recursive algorithms for exact enumerating various diameter no more than d subtrees (abbreviated as DNMT-d subtrees) of T. As applications, we apply these algorithms to derive the number of DNMT-d subtrees in a full binary tree Bh with h≥2 levels, and briefly discuss the density of DNMT-d subtrees in general trees. Our research generalizes the work of Frank Ruskey on Listing and Counting Subtrees of a Tree in 1981 and makes it a special case of our study where d equals the diameter of the tree T. Moreover, the proposed O(dn2) algorithms introduce new approaches for enumerating subtrees under diameter constraints and lay the groundwork for counting diameter-constrained subgraphs (motifs) in complex networks. |
| ArticleNumber | 105353 |
| Author | Li, Bo Jin, Bang-Bang Zhang, Xiao-Dong Zhao, Kai Yang, Yu Sun, Xiaoming Wang, Hua |
| Author_xml | – sequence: 1 givenname: Yu surname: Yang fullname: Yang, Yu email: yangyu@sjtu.edu.cn organization: School of Software, Pingdingshan University, Pingdingshan 467000, China – sequence: 2 givenname: Bang-Bang surname: Jin fullname: Jin, Bang-Bang email: bangbangjin@stu.haut.edu.cn organization: School of Software, Pingdingshan University, Pingdingshan 467000, China – sequence: 3 givenname: Xiaoming surname: Sun fullname: Sun, Xiaoming email: sunxiaoming@ict.ac.cn organization: State Key Lab of Processors, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China – sequence: 4 givenname: Xiao-Dong orcidid: 0000-0003-0783-051X surname: Zhang fullname: Zhang, Xiao-Dong email: xiaodong@sjtu.edu.cn organization: School of Mathematical Sciences, MOE-LSC and SHE-MAC, Shanghai Jiao Tong University, Shanghai, 200240, China – sequence: 5 givenname: Bo surname: Li fullname: Li, Bo email: liboyn@pdsu.edu.cn organization: School of Software, Pingdingshan University, Pingdingshan 467000, China – sequence: 6 givenname: Kai surname: Zhao fullname: Zhao, Kai email: zhaokai@pdsu.edu.cn organization: School of Software, Pingdingshan University, Pingdingshan 467000, China – sequence: 7 givenname: Hua surname: Wang fullname: Wang, Hua email: hwang@georgiasouthern.edu organization: Department of Mathematical Sciences, Georgia Southern University Statesboro, GA 30460, USA |
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| Cites_doi | 10.1080/00207160.2015.1109640 10.1016/j.tcs.2018.09.021 10.1002/jgt.21674 10.1109/TNSE.2021.3108974 10.1126/science.add9330 10.1137/12089394X 10.1016/j.dam.2020.06.013 10.1093/bioinformatics/btn163 10.1093/comjnl/bxaa084 10.1016/j.tcs.2015.02.028 10.1002/jgt.22359 10.1021/ci000095o 10.1145/3433652 10.1002/jgt.22993 10.1109/TSMC.2021.3049278 10.1016/j.jctb.2014.02.003 10.1137/21M1416771 10.1016/j.aam.2004.07.002 10.1016/j.ins.2022.05.038 10.1016/j.tcs.2006.09.002 10.1137/22M1494804 10.1002/jgt.23043 10.1186/s12859-020-3374-4 10.1137/20M1375048 10.1137/0210011 10.1093/bioinformatics/btab875 10.1137/070687736 10.1112/S1461157000000243 10.1186/1752-0509-5-S3-S5 10.1016/j.tcs.2021.09.024 10.1016/j.tcs.2018.08.009 10.1016/j.dam.2021.08.009 10.1016/j.ic.2022.104942 10.1016/j.disc.2023.113654 10.1287/moor.5.3.422 10.1016/j.dam.2025.05.043 10.1016/j.jctb.2024.06.002 10.1016/j.dam.2015.09.025 10.1126/science.298.5594.824 10.1016/j.ic.2017.07.003 10.1016/j.ic.2016.10.004 10.1007/s00453-019-00656-8 10.1126/science.aad9029 10.1016/j.tcs.2022.04.033 10.1016/j.ipl.2022.106302 10.1016/j.dam.2023.06.011 10.1007/s40484-018-0140-y 10.1093/bioadv/vbad015 10.1007/s00453-011-9600-8 |
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| Keywords | Network motifs Diameter constraint Generating function Subtree number Algorithm |
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| References | Qian, Uehara (br0480) 2025; 375 Yang, Li, Jin, Li, Wang, Zhang (br0570) 2021; 892 Ruskey (br0120) 1981; 10 Wu, Liu, Chen, Huang, Zheng, Zhang (br0080) 2021; 52 Xiao, Wang, Liu, Wang, Casseau (br0440) 2020; 68 Linz, John, Semple (br0140) 2013; 42 Poureidi (br0560) 2022; 178 Mai, Mirarab (br0210) 2022; 38 Chen, Hu, Wang (br0020) 2017; 256 Kirk, Wang (br0490) 2008; 22 Chin, Gordon, MacPhee, Vincent (br0260) 2018; 89 Sun, Li, Liu, Wang, Yang (br0420) 2022; 434 Guillemot, Sikora (br0170) 2013; 65 Conte, Grossi, Marino, Versari (br0430) 2020; 82 Milo, Shen-Orr, Itzkovitz, Kashtan, Chklovskii, Alon (br0040) 2002; 298 Yang, Liu, Wang, Feng (br0540) 2016; 203 Winding, Pedigo, Barnes, Patsolic, Park, Kazimiers, Fushiki, Andrade, Khandelwal, Valdes-Aleman (br0070) 2023; 379 Ma, Dehmer, Künzi, Tripathi, Ghorbani, Tao, Emmert-Streib (br0310) 2022; 606 Randic, Zupan (br0320) 2001; 41 Xiao, Zhao, Liu, Mao (br0160) 2017; 94 Iwata, Yokoi (br0470) 2023; 52 Conte, Grossi, Marino, Uno, Versari (br0030) 2022; 51 Xiao, Zhao, Mao, Chen (br0350) 2019; 767 Hu, Ruskey (br0360) 1980; 5 Yang, Liu, Wang, Fu (br0390) 2015; 268 Knudsen (br0190) 2003 Hosoya (br0300) 1986 Pittel (br0240) 2023; 37 Lin, Chen (br0050) 2017; 252 Zhang, Zhang, Gray, Wang (br0500) 2013; 73 Ribeiro, Paredes, Silva, Aparicio, Silva (br0060) 2021; 54 Goldberg, Jerrum (br0370) 2000; 3 Willson, Tabatabaee, Liu, Warnow (br0220) 2023; 3 Székely, Wang (br0330) 2005; 34 Conte, Kanté, Otachi, Uno, Wasa (br0450) 2020; 818 Ingels, Azaïs (br0520) 2022; 922 Knor, Sedlar, Škrekovski, Yang (br0530) 2026; 509 Kim, Li, Wang, Pan (br0110) 2011; 5 Wang (br0290) 2024; 169 Benson, Gleich, Leskovec (br0010) 2016; 353 Yang, Liu, Wang, Scott (br0550) 2015; 580 Nakahata, Nishino, Kawahara, Minato (br0460) 2020 Haslegrave (br0230) 2014; 107 Alon, Dao, Hajirasouliha, Hormozdiari, Sahinalp (br0200) 2008; 24 Luo, Xu, Tian (br0270) 2024; 347 Coff, Chan, Ramsland, Guy (br0180) 2020; 21 Yang, Liu, Wang, Zhang, Chen (br0130) 2022; 289 Yang, Liu, Wang, Deng, Magnant (br0380) 2017; 60 Yang, Jin, Lu, Hui, Zhao, Wang (br0580) 2023; 339 Yan, Yeh (br0340) 2006; 369 Xia, Yu, Liu, Li, Lee (br0090) 2021; 9 Cambie, Chen, Hao, Tokar (br0280) 2024; 105 Li, Luo, Xiao, Liang (br0150) 2018; 6 Yang, Chen, Zhang, Li, Sun, Liu (br0410) 2022; 65 Yang, Sun, Cao, Wang, Zhang (br0400) 2020; 285 Xu, Li, Wang (br0510) 2021; 304 Zhao, Yu, Li, Zhang, Rong (br0100) 2023 Chen, Wei, Lian (br0250) 2023; 104 Knudsen (10.1016/j.ic.2025.105353_br0190) 2003 Chen (10.1016/j.ic.2025.105353_br0250) 2023; 104 Wang (10.1016/j.ic.2025.105353_br0290) 2024; 169 Yang (10.1016/j.ic.2025.105353_br0540) 2016; 203 Xu (10.1016/j.ic.2025.105353_br0510) 2021; 304 Conte (10.1016/j.ic.2025.105353_br0450) 2020; 818 Ma (10.1016/j.ic.2025.105353_br0310) 2022; 606 Qian (10.1016/j.ic.2025.105353_br0480) 2025; 375 Iwata (10.1016/j.ic.2025.105353_br0470) 2023; 52 Yan (10.1016/j.ic.2025.105353_br0340) 2006; 369 Sun (10.1016/j.ic.2025.105353_br0420) 2022; 434 Goldberg (10.1016/j.ic.2025.105353_br0370) 2000; 3 Hu (10.1016/j.ic.2025.105353_br0360) 1980; 5 Yang (10.1016/j.ic.2025.105353_br0380) 2017; 60 Ingels (10.1016/j.ic.2025.105353_br0520) 2022; 922 Ruskey (10.1016/j.ic.2025.105353_br0120) 1981; 10 Alon (10.1016/j.ic.2025.105353_br0200) 2008; 24 Xiao (10.1016/j.ic.2025.105353_br0160) 2017; 94 Xiao (10.1016/j.ic.2025.105353_br0350) 2019; 767 Wu (10.1016/j.ic.2025.105353_br0080) 2021; 52 Xiao (10.1016/j.ic.2025.105353_br0440) 2020; 68 Yang (10.1016/j.ic.2025.105353_br0400) 2020; 285 Zhao (10.1016/j.ic.2025.105353_br0100) 2023 Chen (10.1016/j.ic.2025.105353_br0020) 2017; 256 Lin (10.1016/j.ic.2025.105353_br0050) 2017; 252 Kim (10.1016/j.ic.2025.105353_br0110) 2011; 5 Haslegrave (10.1016/j.ic.2025.105353_br0230) 2014; 107 Luo (10.1016/j.ic.2025.105353_br0270) 2024; 347 Yang (10.1016/j.ic.2025.105353_br0570) 2021; 892 Knor (10.1016/j.ic.2025.105353_br0530) 2026; 509 Conte (10.1016/j.ic.2025.105353_br0030) 2022; 51 Milo (10.1016/j.ic.2025.105353_br0040) 2002; 298 Cambie (10.1016/j.ic.2025.105353_br0280) 2024; 105 Hosoya (10.1016/j.ic.2025.105353_br0300) 1986 Yang (10.1016/j.ic.2025.105353_br0390) 2015; 268 Winding (10.1016/j.ic.2025.105353_br0070) 2023; 379 Yang (10.1016/j.ic.2025.105353_br0550) 2015; 580 Székely (10.1016/j.ic.2025.105353_br0330) 2005; 34 Yang (10.1016/j.ic.2025.105353_br0580) 2023; 339 Kirk (10.1016/j.ic.2025.105353_br0490) 2008; 22 Mai (10.1016/j.ic.2025.105353_br0210) 2022; 38 Benson (10.1016/j.ic.2025.105353_br0010) 2016; 353 Zhang (10.1016/j.ic.2025.105353_br0500) 2013; 73 Guillemot (10.1016/j.ic.2025.105353_br0170) 2013; 65 Linz (10.1016/j.ic.2025.105353_br0140) 2013; 42 Coff (10.1016/j.ic.2025.105353_br0180) 2020; 21 Yang (10.1016/j.ic.2025.105353_br0130) 2022; 289 Willson (10.1016/j.ic.2025.105353_br0220) 2023; 3 Conte (10.1016/j.ic.2025.105353_br0430) 2020; 82 Pittel (10.1016/j.ic.2025.105353_br0240) 2023; 37 Li (10.1016/j.ic.2025.105353_br0150) 2018; 6 Randic (10.1016/j.ic.2025.105353_br0320) 2001; 41 Poureidi (10.1016/j.ic.2025.105353_br0560) 2022; 178 Xia (10.1016/j.ic.2025.105353_br0090) 2021; 9 Ribeiro (10.1016/j.ic.2025.105353_br0060) 2021; 54 Chin (10.1016/j.ic.2025.105353_br0260) 2018; 89 Yang (10.1016/j.ic.2025.105353_br0410) 2022; 65 Nakahata (10.1016/j.ic.2025.105353_br0460) 2020 |
| References_xml | – volume: 285 start-page: 483 year: 2020 end-page: 492 ident: br0400 article-title: The expected subtree number index in random polyphenylene and spiro chains publication-title: Discrete Appl. Math. – volume: 9 start-page: 990 year: 2021 end-page: 1005 ident: br0090 article-title: Chief: clustering with higher-order motifs in big networks publication-title: IEEE Trans. Netw. Sci. Eng. – volume: 347 year: 2024 ident: br0270 article-title: Random subtrees and unimodal sequences in graphs publication-title: Discrete Math. – volume: 178 year: 2022 ident: br0560 article-title: On computing the number of (BC-) subtrees, eccentric subtree number, and global and local means of trees publication-title: Inf. Process. Lett. – volume: 68 start-page: 261 year: 2020 end-page: 265 ident: br0440 article-title: An optimal algorithm for enumerating connected convex subgraphs in acyclic digraphs publication-title: IEEE Trans. Circuits Syst. II, Express Briefs – volume: 252 start-page: 138 year: 2017 end-page: 160 ident: br0050 article-title: The parameterized complexity of publication-title: Inf. Comput. – volume: 38 start-page: 1532 year: 2022 end-page: 1541 ident: br0210 article-title: Completing gene trees without species trees in sub-quadratic time publication-title: Bioinformatics – volume: 434 year: 2022 ident: br0420 article-title: Enumeration of subtrees of planar two-tree networks publication-title: Appl. Math. Comput. – volume: 37 start-page: 1 year: 2023 end-page: 16 ident: br0240 article-title: Expected number of induced subtrees shared by two independent copies of a random tree publication-title: SIAM J. Discrete Math. – volume: 606 start-page: 143 year: 2022 end-page: 151 ident: br0310 article-title: The usefulness of topological indices publication-title: Inf. Sci. – volume: 104 start-page: 645 year: 2023 end-page: 658 ident: br0250 article-title: Solution to a conjecture on the mean subtree order of graphs under edge addition publication-title: J. Graph Theory – start-page: 433 year: 2003 end-page: 446 ident: br0190 article-title: Optimal multiple parsimony alignment with affine gap cost using a phylogenetic tree publication-title: Algorithms in Bioinformatics – volume: 5 start-page: 422 year: 1980 end-page: 434 ident: br0360 article-title: Circular cuts in a network publication-title: Math. Oper. Res. – volume: 65 start-page: 828 year: 2013 end-page: 844 ident: br0170 article-title: Finding and counting vertex-colored subtrees publication-title: Algorithmica – volume: 65 start-page: 554 year: 2022 end-page: 572 ident: br0410 article-title: Algorithms based on path contraction carrying weights for enumerating subtrees of tricyclic graphs publication-title: Comput. J. – year: 2020 ident: br0460 article-title: Enumerating all subgraphs under given constraints using zero-suppressed sentential decision diagrams publication-title: 18th International Symposium on Experimental Algorithms (SEA 2020) – volume: 42 start-page: 1768 year: 2013 end-page: 1776 ident: br0140 article-title: Counting trees in a phylogenetic network is ﹨# p-complete publication-title: SIAM J. Comput. – volume: 580 start-page: 59 year: 2015 end-page: 74 ident: br0550 article-title: Enumeration of BC-subtrees of trees publication-title: Theor. Comput. Sci. – volume: 21 start-page: 1 year: 2020 end-page: 18 ident: br0180 article-title: Identifying glycan motifs using a novel subtree mining approach publication-title: BMC Bioinform. – start-page: 110 year: 1986 end-page: 123 ident: br0300 article-title: Topological index as a common tool for quantum chemistry, statistical mechanics, and graph theory publication-title: Mathematical and Computational Concepts in Chemistry – volume: 5 start-page: 1 year: 2011 end-page: 13 ident: br0110 article-title: Biological network motif detection and evaluation publication-title: BMC Syst. Biol. – volume: 10 start-page: 141 year: 1981 end-page: 150 ident: br0120 article-title: Listing and counting subtrees of a tree publication-title: SIAM J. Comput. – volume: 892 start-page: 258 year: 2021 end-page: 278 ident: br0570 article-title: Enumeration of subtrees and BC-subtrees with maximum degree no more than publication-title: Theor. Comput. Sci. – volume: 52 start-page: 1230 year: 2023 end-page: 1268 ident: br0470 article-title: Finding maximum edge-disjoint paths between multiple terminals publication-title: SIAM J. Comput. – volume: 82 start-page: 1547 year: 2020 end-page: 1573 ident: br0430 article-title: Sublinear-space and bounded-delay algorithms for maximal clique enumeration in graphs publication-title: Algorithmica – volume: 203 start-page: 184 year: 2016 end-page: 203 ident: br0540 article-title: On algorithms for enumerating BC-subtrees of unicyclic and edge-disjoint bicyclic graphs publication-title: Discrete Appl. Math. – volume: 94 start-page: 372 year: 2017 end-page: 385 ident: br0160 article-title: Trees with large numbers of subtrees publication-title: Int. J. Comput. Math. – volume: 41 start-page: 550 year: 2001 end-page: 560 ident: br0320 article-title: On interpretation of well-known topological indices publication-title: J. Chem. Inf. Comput. Sci. – start-page: 1 year: 2023 end-page: 26 ident: br0100 article-title: Learned sketch for subgraph counting: a holistic approach publication-title: VLDB J. – volume: 767 start-page: 16 year: 2019 end-page: 25 ident: br0350 article-title: Invulnerability of planar two-tree networks publication-title: Theor. Comput. Sci. – volume: 73 start-page: 280 year: 2013 end-page: 295 ident: br0500 article-title: The number of subtrees of trees with given degree sequence publication-title: J. Graph Theory – volume: 379 year: 2023 ident: br0070 article-title: The connectome of an insect brain publication-title: Science – volume: 3 year: 2023 ident: br0220 article-title: DISCO+QR: rooting species trees in the presence of GDL and ILS publication-title: Bioinform. Adv. – volume: 339 start-page: 184 year: 2023 end-page: 201 ident: br0580 article-title: Computing the expected subtree number of random hexagonal and phenylene chains based on probability matrices publication-title: Discrete Appl. Math. – volume: 818 start-page: 2 year: 2020 end-page: 11 ident: br0450 article-title: Efficient enumeration of maximal k-degenerate induced subgraphs of a chordal graph publication-title: Theor. Comput. Sci. – volume: 51 start-page: 1580 year: 2022 end-page: 1625 ident: br0030 article-title: Proximity search for maximal subgraph enumeration publication-title: SIAM J. Comput. – volume: 54 start-page: 1 year: 2021 end-page: 36 ident: br0060 article-title: A survey on subgraph counting: concepts, algorithms, and applications to network motifs and graphlets publication-title: ACM Comput. Surv. – volume: 89 start-page: 413 year: 2018 end-page: 438 ident: br0260 article-title: Subtrees of graphs publication-title: J. Graph Theory – volume: 3 start-page: 117 year: 2000 end-page: 124 ident: br0370 article-title: Counting unlabelled subtrees of a tree is #P-complete publication-title: LMS J. Comput. Math. – volume: 169 start-page: 45 year: 2024 end-page: 62 ident: br0290 article-title: On the difference of mean subtree orders under edge contraction publication-title: J. Comb. Theory, Ser. B – volume: 60 start-page: 690 year: 2017 end-page: 710 ident: br0380 article-title: On algorithms for enumerating subtrees of hexagonal and phenylene chains publication-title: Comput. J. – volume: 22 start-page: 985 year: 2008 end-page: 995 ident: br0490 article-title: Largest number of subtrees of trees with a given maximum degree publication-title: SIAM J. Discrete Math. – volume: 34 start-page: 138 year: 2005 end-page: 155 ident: br0330 article-title: On subtrees of trees publication-title: Adv. Appl. Math. – volume: 509 year: 2026 ident: br0530 article-title: Invitation to the subpath number publication-title: Appl. Math. Comput. – volume: 375 start-page: 129 year: 2025 end-page: 138 ident: br0480 article-title: Constant time enumeration of weighted trees publication-title: Discrete Appl. Math. – volume: 298 start-page: 824 year: 2002 end-page: 827 ident: br0040 article-title: Network motifs: simple building blocks of complex networks publication-title: Science – volume: 256 start-page: 160 year: 2017 end-page: 173 ident: br0020 article-title: Finding connected publication-title: Inf. Comput. – volume: 52 start-page: 2237 year: 2021 end-page: 2249 ident: br0080 article-title: Detecting mixing services via mining bitcoin transaction network with hybrid motifs publication-title: IEEE Trans. Syst. Man Cybern. Syst. – volume: 268 start-page: 547 year: 2015 end-page: 560 ident: br0390 article-title: Subtrees of spiro and polyphenyl hexagonal chains publication-title: Appl. Math. Comput. – volume: 304 start-page: 283 year: 2021 end-page: 296 ident: br0510 article-title: The number of subtrees in graphs with given number of cut edges publication-title: Discrete Appl. Math. – volume: 353 start-page: 163 year: 2016 end-page: 166 ident: br0010 article-title: Higher-order organization of complex networks publication-title: Science – volume: 369 start-page: 256 year: 2006 end-page: 268 ident: br0340 article-title: Enumeration of subtrees of trees publication-title: Theor. Comput. Sci. – volume: 289 year: 2022 ident: br0130 article-title: On enumerating algorithms of novel multiple leaf-distance granular regular publication-title: Inf. Comput. – volume: 6 start-page: 142 year: 2018 end-page: 154 ident: br0150 article-title: Mtmo: an efficient network-centric algorithm for subtree counting and enumeration publication-title: Quant. Biol. – volume: 922 start-page: 312 year: 2022 end-page: 334 ident: br0520 article-title: Enumeration of irredundant forests publication-title: Theor. Comput. Sci. – volume: 105 start-page: 357 year: 2024 end-page: 366 ident: br0280 article-title: Decreasing the mean subtree order by adding publication-title: J. Graph Theory – volume: 107 start-page: 26 year: 2014 end-page: 41 ident: br0230 article-title: Extremal results on average subtree density of series-reduced trees publication-title: J. Comb. Theory, Ser. B – volume: 24 start-page: i241 year: 2008 end-page: i249 ident: br0200 article-title: Biomolecular network motif counting and discovery by color coding publication-title: Bioinformatics – volume: 94 start-page: 372 issue: 2 year: 2017 ident: 10.1016/j.ic.2025.105353_br0160 article-title: Trees with large numbers of subtrees publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2015.1109640 – volume: 767 start-page: 16 year: 2019 ident: 10.1016/j.ic.2025.105353_br0350 article-title: Invulnerability of planar two-tree networks publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2018.09.021 – volume: 73 start-page: 280 issue: 3 year: 2013 ident: 10.1016/j.ic.2025.105353_br0500 article-title: The number of subtrees of trees with given degree sequence publication-title: J. Graph Theory doi: 10.1002/jgt.21674 – volume: 9 start-page: 990 issue: 3 year: 2021 ident: 10.1016/j.ic.2025.105353_br0090 article-title: Chief: clustering with higher-order motifs in big networks publication-title: IEEE Trans. Netw. Sci. Eng. doi: 10.1109/TNSE.2021.3108974 – year: 2020 ident: 10.1016/j.ic.2025.105353_br0460 article-title: Enumerating all subgraphs under given constraints using zero-suppressed sentential decision diagrams – volume: 379 issue: 6636 year: 2023 ident: 10.1016/j.ic.2025.105353_br0070 article-title: The connectome of an insect brain publication-title: Science doi: 10.1126/science.add9330 – volume: 42 start-page: 1768 issue: 4 year: 2013 ident: 10.1016/j.ic.2025.105353_br0140 article-title: Counting trees in a phylogenetic network is ﹨# p-complete publication-title: SIAM J. Comput. doi: 10.1137/12089394X – volume: 285 start-page: 483 year: 2020 ident: 10.1016/j.ic.2025.105353_br0400 article-title: The expected subtree number index in random polyphenylene and spiro chains publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2020.06.013 – volume: 24 start-page: i241 issue: 13 year: 2008 ident: 10.1016/j.ic.2025.105353_br0200 article-title: Biomolecular network motif counting and discovery by color coding publication-title: Bioinformatics doi: 10.1093/bioinformatics/btn163 – volume: 65 start-page: 554 issue: 3 year: 2022 ident: 10.1016/j.ic.2025.105353_br0410 article-title: Algorithms based on path contraction carrying weights for enumerating subtrees of tricyclic graphs publication-title: Comput. J. doi: 10.1093/comjnl/bxaa084 – volume: 580 start-page: 59 year: 2015 ident: 10.1016/j.ic.2025.105353_br0550 article-title: Enumeration of BC-subtrees of trees publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2015.02.028 – volume: 89 start-page: 413 year: 2018 ident: 10.1016/j.ic.2025.105353_br0260 article-title: Subtrees of graphs publication-title: J. Graph Theory doi: 10.1002/jgt.22359 – volume: 41 start-page: 550 issue: 3 year: 2001 ident: 10.1016/j.ic.2025.105353_br0320 article-title: On interpretation of well-known topological indices publication-title: J. Chem. Inf. Comput. Sci. doi: 10.1021/ci000095o – volume: 54 start-page: 1 issue: 2 year: 2021 ident: 10.1016/j.ic.2025.105353_br0060 article-title: A survey on subgraph counting: concepts, algorithms, and applications to network motifs and graphlets publication-title: ACM Comput. Surv. doi: 10.1145/3433652 – volume: 509 year: 2026 ident: 10.1016/j.ic.2025.105353_br0530 article-title: Invitation to the subpath number publication-title: Appl. Math. Comput. – volume: 68 start-page: 261 issue: 1 year: 2020 ident: 10.1016/j.ic.2025.105353_br0440 article-title: An optimal algorithm for enumerating connected convex subgraphs in acyclic digraphs publication-title: IEEE Trans. Circuits Syst. II, Express Briefs – volume: 104 start-page: 645 issue: 3 year: 2023 ident: 10.1016/j.ic.2025.105353_br0250 article-title: Solution to a conjecture on the mean subtree order of graphs under edge addition publication-title: J. Graph Theory doi: 10.1002/jgt.22993 – volume: 52 start-page: 2237 issue: 4 year: 2021 ident: 10.1016/j.ic.2025.105353_br0080 article-title: Detecting mixing services via mining bitcoin transaction network with hybrid motifs publication-title: IEEE Trans. Syst. Man Cybern. Syst. doi: 10.1109/TSMC.2021.3049278 – volume: 107 start-page: 26 year: 2014 ident: 10.1016/j.ic.2025.105353_br0230 article-title: Extremal results on average subtree density of series-reduced trees publication-title: J. Comb. Theory, Ser. B doi: 10.1016/j.jctb.2014.02.003 – volume: 37 start-page: 1 issue: 1 year: 2023 ident: 10.1016/j.ic.2025.105353_br0240 article-title: Expected number of induced subtrees shared by two independent copies of a random tree publication-title: SIAM J. Discrete Math. doi: 10.1137/21M1416771 – start-page: 110 year: 1986 ident: 10.1016/j.ic.2025.105353_br0300 article-title: Topological index as a common tool for quantum chemistry, statistical mechanics, and graph theory – volume: 34 start-page: 138 issue: 1 year: 2005 ident: 10.1016/j.ic.2025.105353_br0330 article-title: On subtrees of trees publication-title: Adv. Appl. Math. doi: 10.1016/j.aam.2004.07.002 – volume: 606 start-page: 143 year: 2022 ident: 10.1016/j.ic.2025.105353_br0310 article-title: The usefulness of topological indices publication-title: Inf. Sci. doi: 10.1016/j.ins.2022.05.038 – volume: 369 start-page: 256 issue: 1 year: 2006 ident: 10.1016/j.ic.2025.105353_br0340 article-title: Enumeration of subtrees of trees publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2006.09.002 – volume: 52 start-page: 1230 issue: 5 year: 2023 ident: 10.1016/j.ic.2025.105353_br0470 article-title: Finding maximum edge-disjoint paths between multiple terminals publication-title: SIAM J. Comput. doi: 10.1137/22M1494804 – volume: 105 start-page: 357 issue: 3 year: 2024 ident: 10.1016/j.ic.2025.105353_br0280 article-title: Decreasing the mean subtree order by adding k edges publication-title: J. Graph Theory doi: 10.1002/jgt.23043 – volume: 21 start-page: 1 year: 2020 ident: 10.1016/j.ic.2025.105353_br0180 article-title: Identifying glycan motifs using a novel subtree mining approach publication-title: BMC Bioinform. doi: 10.1186/s12859-020-3374-4 – volume: 51 start-page: 1580 issue: 5 year: 2022 ident: 10.1016/j.ic.2025.105353_br0030 article-title: Proximity search for maximal subgraph enumeration publication-title: SIAM J. Comput. doi: 10.1137/20M1375048 – volume: 268 start-page: 547 year: 2015 ident: 10.1016/j.ic.2025.105353_br0390 article-title: Subtrees of spiro and polyphenyl hexagonal chains publication-title: Appl. Math. Comput. – start-page: 1 year: 2023 ident: 10.1016/j.ic.2025.105353_br0100 article-title: Learned sketch for subgraph counting: a holistic approach publication-title: VLDB J. – volume: 10 start-page: 141 issue: 1 year: 1981 ident: 10.1016/j.ic.2025.105353_br0120 article-title: Listing and counting subtrees of a tree publication-title: SIAM J. Comput. doi: 10.1137/0210011 – volume: 38 start-page: 1532 issue: 6 year: 2022 ident: 10.1016/j.ic.2025.105353_br0210 article-title: Completing gene trees without species trees in sub-quadratic time publication-title: Bioinformatics doi: 10.1093/bioinformatics/btab875 – volume: 22 start-page: 985 issue: 3 year: 2008 ident: 10.1016/j.ic.2025.105353_br0490 article-title: Largest number of subtrees of trees with a given maximum degree publication-title: SIAM J. Discrete Math. doi: 10.1137/070687736 – volume: 3 start-page: 117 year: 2000 ident: 10.1016/j.ic.2025.105353_br0370 article-title: Counting unlabelled subtrees of a tree is #P-complete publication-title: LMS J. Comput. Math. doi: 10.1112/S1461157000000243 – volume: 434 year: 2022 ident: 10.1016/j.ic.2025.105353_br0420 article-title: Enumeration of subtrees of planar two-tree networks publication-title: Appl. Math. Comput. – volume: 5 start-page: 1 year: 2011 ident: 10.1016/j.ic.2025.105353_br0110 article-title: Biological network motif detection and evaluation publication-title: BMC Syst. Biol. doi: 10.1186/1752-0509-5-S3-S5 – volume: 892 start-page: 258 year: 2021 ident: 10.1016/j.ic.2025.105353_br0570 article-title: Enumeration of subtrees and BC-subtrees with maximum degree no more than k in trees publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2021.09.024 – volume: 818 start-page: 2 year: 2020 ident: 10.1016/j.ic.2025.105353_br0450 article-title: Efficient enumeration of maximal k-degenerate induced subgraphs of a chordal graph publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2018.08.009 – volume: 304 start-page: 283 year: 2021 ident: 10.1016/j.ic.2025.105353_br0510 article-title: The number of subtrees in graphs with given number of cut edges publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2021.08.009 – volume: 289 year: 2022 ident: 10.1016/j.ic.2025.105353_br0130 article-title: On enumerating algorithms of novel multiple leaf-distance granular regular α-subtrees of trees publication-title: Inf. Comput. doi: 10.1016/j.ic.2022.104942 – volume: 347 issue: 1 year: 2024 ident: 10.1016/j.ic.2025.105353_br0270 article-title: Random subtrees and unimodal sequences in graphs publication-title: Discrete Math. doi: 10.1016/j.disc.2023.113654 – volume: 5 start-page: 422 issue: 3 year: 1980 ident: 10.1016/j.ic.2025.105353_br0360 article-title: Circular cuts in a network publication-title: Math. Oper. Res. doi: 10.1287/moor.5.3.422 – volume: 375 start-page: 129 year: 2025 ident: 10.1016/j.ic.2025.105353_br0480 article-title: Constant time enumeration of weighted trees publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2025.05.043 – volume: 169 start-page: 45 year: 2024 ident: 10.1016/j.ic.2025.105353_br0290 article-title: On the difference of mean subtree orders under edge contraction publication-title: J. Comb. Theory, Ser. B doi: 10.1016/j.jctb.2024.06.002 – volume: 203 start-page: 184 year: 2016 ident: 10.1016/j.ic.2025.105353_br0540 article-title: On algorithms for enumerating BC-subtrees of unicyclic and edge-disjoint bicyclic graphs publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2015.09.025 – volume: 298 start-page: 824 issue: 5594 year: 2002 ident: 10.1016/j.ic.2025.105353_br0040 article-title: Network motifs: simple building blocks of complex networks publication-title: Science doi: 10.1126/science.298.5594.824 – volume: 256 start-page: 160 year: 2017 ident: 10.1016/j.ic.2025.105353_br0020 article-title: Finding connected k-subgraphs with high density publication-title: Inf. Comput. doi: 10.1016/j.ic.2017.07.003 – volume: 252 start-page: 138 year: 2017 ident: 10.1016/j.ic.2025.105353_br0050 article-title: The parameterized complexity of k-edge induced subgraphs publication-title: Inf. Comput. doi: 10.1016/j.ic.2016.10.004 – volume: 82 start-page: 1547 issue: 6 year: 2020 ident: 10.1016/j.ic.2025.105353_br0430 article-title: Sublinear-space and bounded-delay algorithms for maximal clique enumeration in graphs publication-title: Algorithmica doi: 10.1007/s00453-019-00656-8 – volume: 60 start-page: 690 issue: 5 year: 2017 ident: 10.1016/j.ic.2025.105353_br0380 article-title: On algorithms for enumerating subtrees of hexagonal and phenylene chains publication-title: Comput. J. – volume: 353 start-page: 163 issue: 6295 year: 2016 ident: 10.1016/j.ic.2025.105353_br0010 article-title: Higher-order organization of complex networks publication-title: Science doi: 10.1126/science.aad9029 – volume: 922 start-page: 312 year: 2022 ident: 10.1016/j.ic.2025.105353_br0520 article-title: Enumeration of irredundant forests publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2022.04.033 – volume: 178 year: 2022 ident: 10.1016/j.ic.2025.105353_br0560 article-title: On computing the number of (BC-) subtrees, eccentric subtree number, and global and local means of trees publication-title: Inf. Process. Lett. doi: 10.1016/j.ipl.2022.106302 – volume: 339 start-page: 184 year: 2023 ident: 10.1016/j.ic.2025.105353_br0580 article-title: Computing the expected subtree number of random hexagonal and phenylene chains based on probability matrices publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2023.06.011 – volume: 6 start-page: 142 year: 2018 ident: 10.1016/j.ic.2025.105353_br0150 article-title: Mtmo: an efficient network-centric algorithm for subtree counting and enumeration publication-title: Quant. Biol. doi: 10.1007/s40484-018-0140-y – start-page: 433 year: 2003 ident: 10.1016/j.ic.2025.105353_br0190 article-title: Optimal multiple parsimony alignment with affine gap cost using a phylogenetic tree – volume: 3 issue: 1 year: 2023 ident: 10.1016/j.ic.2025.105353_br0220 article-title: DISCO+QR: rooting species trees in the presence of GDL and ILS publication-title: Bioinform. Adv. doi: 10.1093/bioadv/vbad015 – volume: 65 start-page: 828 year: 2013 ident: 10.1016/j.ic.2025.105353_br0170 article-title: Finding and counting vertex-colored subtrees publication-title: Algorithmica doi: 10.1007/s00453-011-9600-8 |
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