Spectral properties of token graphs
Let G be a graph on n vertices. For a given integer k such that 1≤k≤n, the k-token graph Fk(G) of G is defined as the graph whose vertices are the k-subsets of the vertex set of G, and two of them are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this article,...
Uloženo v:
| Vydáno v: | Linear algebra and its applications Ročník 687; s. 181 - 206 |
|---|---|
| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
15.04.2024
|
| Témata: | |
| ISSN: | 0024-3795, 1873-1856 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Let G be a graph on n vertices. For a given integer k such that 1≤k≤n, the k-token graph Fk(G) of G is defined as the graph whose vertices are the k-subsets of the vertex set of G, and two of them are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this article, we study the structural and spectral properties of token graphs. We describe the adjacency matrix and the Laplacian matrix of Fk(G) and obtain bounds on the adjacency and Laplacian spectral radii of Fk(G). Interestingly, it is found that Sn, the star graph on n vertices, has the same Laplacian spectral radius as that of Fk(Sn). It was conjectured that for any graph G, the algebraic connectivity of Fk(G) is equal to the algebraic connectivity of G. This result turned out to be a theorem, as it was proved by using the theory of the continuous Markov chain of random walks and the interchange process. However, proving this theorem using algebraic and combinatorial methods is still an open and interesting problem. Using combinatorial techniques, we prove that the theorem holds for a class of graphs that have a cut-vertex of degree n−1. We also prove it by restricting the smallest degree of the k-token graph of G. |
|---|---|
| AbstractList | Let G be a graph on n vertices. For a given integer k such that 1≤k≤n, the k-token graph Fk(G) of G is defined as the graph whose vertices are the k-subsets of the vertex set of G, and two of them are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this article, we study the structural and spectral properties of token graphs. We describe the adjacency matrix and the Laplacian matrix of Fk(G) and obtain bounds on the adjacency and Laplacian spectral radii of Fk(G). Interestingly, it is found that Sn, the star graph on n vertices, has the same Laplacian spectral radius as that of Fk(Sn). It was conjectured that for any graph G, the algebraic connectivity of Fk(G) is equal to the algebraic connectivity of G. This result turned out to be a theorem, as it was proved by using the theory of the continuous Markov chain of random walks and the interchange process. However, proving this theorem using algebraic and combinatorial methods is still an open and interesting problem. Using combinatorial techniques, we prove that the theorem holds for a class of graphs that have a cut-vertex of degree n−1. We also prove it by restricting the smallest degree of the k-token graph of G. |
| Author | Verma, Piyush Barik, Sasmita |
| Author_xml | – sequence: 1 givenname: Sasmita orcidid: 0000-0002-3927-5218 surname: Barik fullname: Barik, Sasmita email: sasmita@iitbbs.ac.in – sequence: 2 givenname: Piyush surname: Verma fullname: Verma, Piyush email: s21ma09010@iitbbs.ac.in |
| BookMark | eNp9kE1LxDAQhoOsYHf1B3greG6dpB9p8SSLX7DgQT2HaTLV1NqUpAj-e7OsJw97msM7zzDPu2aryU3E2CWHnAOvr4d8RMwFiDIHkQOUJyzhjSwy3lT1iiUQk6yQbXXG1iEMEDckiIRdvcykF49jOns3k18shdT16eI-aUrfPc4f4Zyd9jgGuvibG_Z2f_e6fcx2zw9P29tdpkUrl6yTDSB2umzqxhRdi7rjLUJlTIM9CBIxLSpT91rUFUpjipqXhroOI6ABig2Th7vauxA89UrbBRfrpvigHRUHtXdVg4quau-qQKhoEkn-j5y9_UL_c5S5OTAUlb4teRW0pUmTsT5WooyzR-hfRFpubQ |
| CitedBy_id | crossref_primary_10_1016_j_dam_2025_06_057 crossref_primary_10_1016_j_disc_2024_114382 |
| Cites_doi | 10.1103/PhysRevLett.85.5468 10.1007/s003730200055 10.1016/j.laa.2004.01.020 10.1080/03081080600679029 10.1090/S0894-0347-10-00659-4 10.1016/j.dam.2018.03.085 10.1038/35065725 10.1016/0024-3795(95)00199-2 10.1063/1.5084136 10.7151/dmgt.1959 10.1016/j.laa.2021.05.005 10.1016/j.jctb.2010.07.001 10.1016/j.physa.2014.02.043 10.1137/S0895480191222653 10.26493/2590-9770.1244.720 10.21136/CMJ.1973.101168 10.1016/j.jctb.2006.04.002 10.1016/j.laa.2006.08.017 10.1007/s00373-011-1055-9 |
| ContentType | Journal Article |
| Copyright | 2024 Elsevier Inc. |
| Copyright_xml | – notice: 2024 Elsevier Inc. |
| DBID | AAYXX CITATION |
| DOI | 10.1016/j.laa.2024.02.004 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1873-1856 |
| EndPage | 206 |
| ExternalDocumentID | 10_1016_j_laa_2024_02_004 S0024379524000429 |
| GroupedDBID | --K --M --Z -~X .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 6TJ 7-5 71M 8P~ 9JN AACTN AAEDW AAFTH AAIAV AAIKJ AAKOC AALRI AAOAW AASFE AAXUO ABAOU ABJNI ABMAC ABYKQ ACAZW ACDAQ ACGFS ACRLP ADBBV ADEZE AEBSH AEKER AENEX AFKWA AFTJW AGUBO AGYEJ AHHHB AIEXJ AIGVJ AIKHN AITUG AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ ARUGR AXJTR BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EO8 EO9 EP2 EP3 F5P FDB FEDTE FIRID FNPLU FYGXN G-Q GBLVA HVGLF IHE IXB J1W KOM MCRUF MHUIS MO0 N9A O-L O9- OAUVE OK1 OZT P-8 P-9 P2P PC. Q38 RNS ROL RPZ SDF SDG SES SEW SPC SPCBC SSW T5K TN5 TWZ WH7 XPP YQT ZMT ~G- 29L 5VS 9DU AAEDT AAQFI AAQXK AATTM AAXKI AAYWO AAYXX ABDPE ABEFU ABFNM ABWVN ABXDB ACLOT ACRPL ACVFH ADCNI ADIYS ADMUD ADNMO ADVLN AEIPS AETEA AEUPX AEXQZ AFFNX AFJKZ AFPUW AGHFR AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS EJD FA8 FGOYB G-2 HZ~ M26 M41 MVM OHT R2- SSZ T9H WUQ ~HD |
| ID | FETCH-LOGICAL-c297t-b780aabc4868d3b9acb19a05dd8af02e20aa35d6fc265a7dd3614debba868c003 |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001184555300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0024-3795 |
| IngestDate | Tue Nov 18 20:50:45 EST 2025 Sat Nov 29 07:31:22 EST 2025 Sat Feb 24 15:49:00 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | 05C10 05C75 05C50 Laplacian spectrum Spectral radius Algebraic connectivity Token graph Adjacency spectrum |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c297t-b780aabc4868d3b9acb19a05dd8af02e20aa35d6fc265a7dd3614debba868c003 |
| ORCID | 0000-0002-3927-5218 |
| PageCount | 26 |
| ParticipantIDs | crossref_citationtrail_10_1016_j_laa_2024_02_004 crossref_primary_10_1016_j_laa_2024_02_004 elsevier_sciencedirect_doi_10_1016_j_laa_2024_02_004 |
| PublicationCentury | 2000 |
| PublicationDate | 2024-04-15 |
| PublicationDateYYYYMMDD | 2024-04-15 |
| PublicationDate_xml | – month: 04 year: 2024 text: 2024-04-15 day: 15 |
| PublicationDecade | 2020 |
| PublicationTitle | Linear algebra and its applications |
| PublicationYear | 2024 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Alavi, Lick, Liu (br0010) 2002; 18 Dalfó, Duque, Fabila-Monroy, Fiol, Huemer, Trujillo-Negrete, Zaragoza Martinez (br0110) 2021; 625 Reyes, Dalfó, Fiol, Messegué (br0290) 2023 Haemers (br0220) 1995; 226–228 Audenaert, Godsil, Royle, Rudolph (br0030) 2007; 97 Lew (br0240) 2023 Strogatz (br0320) 2001; 410 Yu, Lu, Tian (br0330) 2004; 387 Callaway, Newman, Strogatz, Watts (br0080) 2000; 85 Barik, Lal, Pati (br0060) 2008; 56 Reyes, Dalfó, Fiol (br0280) 2023 Grone, Merris (br0210) 1994; 7 de Abreu (br0140) 2007; 423 Godsil, Royle (br0190) 2001 Fiedler (br0180) 1973; 23 Fabila-Monroy, Leaños, Trujillo-Negrete (br0170) 2022 Bapat (br0040) 2014 Horn, Johnson (br0230) 2012 Gómez Soto, Leaños, Ríos-Castro, Rivera (br0200) 2018; 247 Brouwer, Haemers (br0070) 2011 Alzaga, Iglesias, Pignol (br0020) 2010; 100 Barghi, Ponomarenko (br0050) 2009; 16 Rudolph (br0310) 2002 Ouyang (br0270) 2019; 60 Dalfó, Fiol (br0120) 2022 Mohar (br0260) 1997; vol. 497 Fabila-Monroy, Flores-Peñaloza, Huemer, Hurtado, Urrutia, Wood, Graphs (br0160) 2012; 28 Caputo, Liggett, Richthammer (br0090) 2010; 23 Dalfó, Fiol, Messegué (br0130) 2023 Carballosa, Fabila-Monroy, Leaños, Rivera (br0100) 2017; 37 Martín-Hernández, Wang, Van Mieghem, D'Agostino (br0250) 2014; 404 de Alba, Carballosa, Leaños, Rivera (br0150) 2020; 76 Rivera, Trujillo-Negrete (br0300) 2018; 1 de Abreu (10.1016/j.laa.2024.02.004_br0140) 2007; 423 Audenaert (10.1016/j.laa.2024.02.004_br0030) 2007; 97 Martín-Hernández (10.1016/j.laa.2024.02.004_br0250) 2014; 404 Carballosa (10.1016/j.laa.2024.02.004_br0100) 2017; 37 Lew (10.1016/j.laa.2024.02.004_br0240) Gómez Soto (10.1016/j.laa.2024.02.004_br0200) 2018; 247 Godsil (10.1016/j.laa.2024.02.004_br0190) 2001 Reyes (10.1016/j.laa.2024.02.004_br0280) Reyes (10.1016/j.laa.2024.02.004_br0290) Barghi (10.1016/j.laa.2024.02.004_br0050) 2009; 16 Caputo (10.1016/j.laa.2024.02.004_br0090) 2010; 23 Dalfó (10.1016/j.laa.2024.02.004_br0110) 2021; 625 Alzaga (10.1016/j.laa.2024.02.004_br0020) 2010; 100 Dalfó (10.1016/j.laa.2024.02.004_br0120) Fabila-Monroy (10.1016/j.laa.2024.02.004_br0170) Mohar (10.1016/j.laa.2024.02.004_br0260) 1997; vol. 497 Dalfó (10.1016/j.laa.2024.02.004_br0130) Fiedler (10.1016/j.laa.2024.02.004_br0180) 1973; 23 Yu (10.1016/j.laa.2024.02.004_br0330) 2004; 387 Callaway (10.1016/j.laa.2024.02.004_br0080) 2000; 85 de Alba (10.1016/j.laa.2024.02.004_br0150) 2020; 76 Fabila-Monroy (10.1016/j.laa.2024.02.004_br0160) 2012; 28 Strogatz (10.1016/j.laa.2024.02.004_br0320) 2001; 410 Bapat (10.1016/j.laa.2024.02.004_br0040) 2014 Horn (10.1016/j.laa.2024.02.004_br0230) 2012 Alavi (10.1016/j.laa.2024.02.004_br0010) 2002; 18 Brouwer (10.1016/j.laa.2024.02.004_br0070) 2011 Grone (10.1016/j.laa.2024.02.004_br0210) 1994; 7 Rivera (10.1016/j.laa.2024.02.004_br0300) 2018; 1 Rudolph (10.1016/j.laa.2024.02.004_br0310) Haemers (10.1016/j.laa.2024.02.004_br0220) 1995; 226–228 Barik (10.1016/j.laa.2024.02.004_br0060) 2008; 56 Ouyang (10.1016/j.laa.2024.02.004_br0270) 2019; 60 |
| References_xml | – year: 2001 ident: br0190 article-title: Algebraic Graph Theory – volume: 7 start-page: 221 year: 1994 end-page: 229 ident: br0210 article-title: The Laplacian spectrum of graph II publication-title: SIAM J. Discrete Math. – year: 2023 ident: br0290 article-title: On the spectra of token graphs of cycles and other graphs – volume: 387 start-page: 41 year: 2004 end-page: 49 ident: br0330 article-title: On the spectral radius of graphs publication-title: Linear Algebra Appl. – volume: 18 start-page: 709 year: 2002 end-page: 715 ident: br0010 article-title: Survey of double vertex graphs publication-title: Graphs Comb. – year: 2022 ident: br0120 article-title: On the algebraic connectivity of token graphs – volume: vol. 497 start-page: 225 year: 1997 end-page: 275 ident: br0260 article-title: Some applications of Laplace eigenvalues of graphs publication-title: Graph Symmetry – volume: 56 start-page: 597 year: 2008 end-page: 610 ident: br0060 article-title: On trees with Laplacian eigenvalue one publication-title: Linear Multilinear Algebra – volume: 410 start-page: 268 year: 2001 end-page: 276 ident: br0320 article-title: Exploring complex networks publication-title: Nature – volume: 16 year: 2009 ident: br0050 article-title: Non-isomorphic graphs with cospectral symmetric powers publication-title: Electron. J. Comb. – volume: 100 start-page: 671 year: 2010 end-page: 682 ident: br0020 article-title: Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements publication-title: J. Comb. Theory, Ser. B – volume: 226–228 start-page: 593 year: 1995 end-page: 616 ident: br0220 article-title: Interlacing eigenvalues and graphs publication-title: Linear Algebra Appl. – year: 2023 ident: br0130 article-title: Some bounds on the Laplacian eigenvalues of token graphs – volume: 76 start-page: 387 year: 2020 end-page: 403 ident: br0150 article-title: Independence and matching numbers of some token graphs publication-title: Australas. J. Comb. – volume: 404 start-page: 92 year: 2014 end-page: 105 ident: br0250 article-title: Algebraic connectivity of interdependent networks publication-title: Phys. A, Stat. Mech. Appl. – volume: 1 year: 2018 ident: br0300 article-title: Hamiltonicity of token graphs of fan graphs publication-title: Art Discrete Appl. Math. – year: 2023 ident: br0280 article-title: On the spectra and spectral radius of token graphs – volume: 85 start-page: 5468 year: 2000 end-page: 5471 ident: br0080 article-title: Network robustness and fragility: percolation on random graphs publication-title: Phys. Rev. Lett. – volume: 23 start-page: 831 year: 2010 end-page: 851 ident: br0090 article-title: Proof of Aldous' spectral gap conjecture publication-title: J. Am. Math. Soc. – volume: 23 start-page: 298 year: 1973 end-page: 305 ident: br0180 article-title: Algebraic connectivity of graphs publication-title: Czechoslov. Math. J. – year: 2014 ident: br0040 article-title: Graphs and Matrices – year: 2011 ident: br0070 article-title: Spectra of Graphs – year: 2023 ident: br0240 article-title: Garland's method for token graphs – volume: 625 start-page: 322 year: 2021 end-page: 348 ident: br0110 article-title: On the Laplacian spectra of token graphs publication-title: Linear Algebra Appl. – volume: 97 start-page: 74 year: 2007 end-page: 90 ident: br0030 article-title: Symmetric squares of graphs publication-title: J. Comb. Theory, Ser. B – volume: 60 year: 2019 ident: br0270 article-title: Computing spectral bounds of the Heisenberg ferromagnet from geometric consideration publication-title: J. Math. Phys. – volume: 247 start-page: 327 year: 2018 end-page: 340 ident: br0200 article-title: The packing number of the double vertex graph of the path graph publication-title: Discrete Appl. Math. – year: 2002 ident: br0310 article-title: Constructing physically intuitive graph invariants – volume: 423 start-page: 53 year: 2007 end-page: 73 ident: br0140 article-title: Old and new results on algebraic connectivity of graphs publication-title: Linear Algebra Appl. – year: 2022 ident: br0170 article-title: On the connectivity of token graphs of trees – year: 2012 ident: br0230 article-title: Matrix Analysis – volume: 28 start-page: 365 year: 2012 end-page: 380 ident: br0160 publication-title: Graphs Comb. – volume: 37 start-page: 573 year: 2017 end-page: 586 ident: br0100 article-title: Regularity and planarity of token graphs publication-title: Discuss. Math., Graph Theory – ident: 10.1016/j.laa.2024.02.004_br0170 – volume: 85 start-page: 5468 issue: 25 year: 2000 ident: 10.1016/j.laa.2024.02.004_br0080 article-title: Network robustness and fragility: percolation on random graphs publication-title: Phys. Rev. Lett. doi: 10.1103/PhysRevLett.85.5468 – volume: 18 start-page: 709 year: 2002 ident: 10.1016/j.laa.2024.02.004_br0010 article-title: Survey of double vertex graphs publication-title: Graphs Comb. doi: 10.1007/s003730200055 – ident: 10.1016/j.laa.2024.02.004_br0280 – volume: 76 start-page: 387 issue: 3 year: 2020 ident: 10.1016/j.laa.2024.02.004_br0150 article-title: Independence and matching numbers of some token graphs publication-title: Australas. J. Comb. – volume: 387 start-page: 41 year: 2004 ident: 10.1016/j.laa.2024.02.004_br0330 article-title: On the spectral radius of graphs publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2004.01.020 – volume: 56 start-page: 597 issue: 6 year: 2008 ident: 10.1016/j.laa.2024.02.004_br0060 article-title: On trees with Laplacian eigenvalue one publication-title: Linear Multilinear Algebra doi: 10.1080/03081080600679029 – volume: 23 start-page: 831 issue: 3 year: 2010 ident: 10.1016/j.laa.2024.02.004_br0090 article-title: Proof of Aldous' spectral gap conjecture publication-title: J. Am. Math. Soc. doi: 10.1090/S0894-0347-10-00659-4 – volume: 247 start-page: 327 year: 2018 ident: 10.1016/j.laa.2024.02.004_br0200 article-title: The packing number of the double vertex graph of the path graph publication-title: Discrete Appl. Math. doi: 10.1016/j.dam.2018.03.085 – volume: 410 start-page: 268 year: 2001 ident: 10.1016/j.laa.2024.02.004_br0320 article-title: Exploring complex networks publication-title: Nature doi: 10.1038/35065725 – volume: 226–228 start-page: 593 year: 1995 ident: 10.1016/j.laa.2024.02.004_br0220 article-title: Interlacing eigenvalues and graphs publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(95)00199-2 – volume: 60 issue: 7 year: 2019 ident: 10.1016/j.laa.2024.02.004_br0270 article-title: Computing spectral bounds of the Heisenberg ferromagnet from geometric consideration publication-title: J. Math. Phys. doi: 10.1063/1.5084136 – year: 2001 ident: 10.1016/j.laa.2024.02.004_br0190 – ident: 10.1016/j.laa.2024.02.004_br0290 – ident: 10.1016/j.laa.2024.02.004_br0130 – volume: vol. 497 start-page: 225 year: 1997 ident: 10.1016/j.laa.2024.02.004_br0260 article-title: Some applications of Laplace eigenvalues of graphs – volume: 37 start-page: 573 issue: 3 year: 2017 ident: 10.1016/j.laa.2024.02.004_br0100 article-title: Regularity and planarity of token graphs publication-title: Discuss. Math., Graph Theory doi: 10.7151/dmgt.1959 – volume: 625 start-page: 322 year: 2021 ident: 10.1016/j.laa.2024.02.004_br0110 article-title: On the Laplacian spectra of token graphs publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2021.05.005 – year: 2012 ident: 10.1016/j.laa.2024.02.004_br0230 – ident: 10.1016/j.laa.2024.02.004_br0240 – ident: 10.1016/j.laa.2024.02.004_br0310 – year: 2011 ident: 10.1016/j.laa.2024.02.004_br0070 – ident: 10.1016/j.laa.2024.02.004_br0120 – volume: 100 start-page: 671 issue: 6 year: 2010 ident: 10.1016/j.laa.2024.02.004_br0020 article-title: Spectra of symmetric powers of graphs and the Weisfeiler-Lehman refinements publication-title: J. Comb. Theory, Ser. B doi: 10.1016/j.jctb.2010.07.001 – year: 2014 ident: 10.1016/j.laa.2024.02.004_br0040 – volume: 404 start-page: 92 year: 2014 ident: 10.1016/j.laa.2024.02.004_br0250 article-title: Algebraic connectivity of interdependent networks publication-title: Phys. A, Stat. Mech. Appl. doi: 10.1016/j.physa.2014.02.043 – volume: 7 start-page: 221 issue: 2 year: 1994 ident: 10.1016/j.laa.2024.02.004_br0210 article-title: The Laplacian spectrum of graph II publication-title: SIAM J. Discrete Math. doi: 10.1137/S0895480191222653 – volume: 1 year: 2018 ident: 10.1016/j.laa.2024.02.004_br0300 article-title: Hamiltonicity of token graphs of fan graphs publication-title: Art Discrete Appl. Math. doi: 10.26493/2590-9770.1244.720 – volume: 16 issue: 1 year: 2009 ident: 10.1016/j.laa.2024.02.004_br0050 article-title: Non-isomorphic graphs with cospectral symmetric powers publication-title: Electron. J. Comb. – volume: 23 start-page: 298 issue: 2 year: 1973 ident: 10.1016/j.laa.2024.02.004_br0180 article-title: Algebraic connectivity of graphs publication-title: Czechoslov. Math. J. doi: 10.21136/CMJ.1973.101168 – volume: 97 start-page: 74 issue: 1 year: 2007 ident: 10.1016/j.laa.2024.02.004_br0030 article-title: Symmetric squares of graphs publication-title: J. Comb. Theory, Ser. B doi: 10.1016/j.jctb.2006.04.002 – volume: 423 start-page: 53 issue: 1 year: 2007 ident: 10.1016/j.laa.2024.02.004_br0140 article-title: Old and new results on algebraic connectivity of graphs publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2006.08.017 – volume: 28 start-page: 365 issue: 3 year: 2012 ident: 10.1016/j.laa.2024.02.004_br0160 publication-title: Graphs Comb. doi: 10.1007/s00373-011-1055-9 |
| SSID | ssj0004702 |
| Score | 2.4004536 |
| Snippet | Let G be a graph on n vertices. For a given integer k such that 1≤k≤n, the k-token graph Fk(G) of G is defined as the graph whose vertices are the k-subsets of... |
| SourceID | crossref elsevier |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 181 |
| SubjectTerms | Adjacency spectrum Algebraic connectivity Laplacian spectrum Spectral radius Token graph |
| Title | Spectral properties of token graphs |
| URI | https://dx.doi.org/10.1016/j.laa.2024.02.004 |
| Volume | 687 |
| WOSCitedRecordID | wos001184555300001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1873-1856 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004702 issn: 0024-3795 databaseCode: AIEXJ dateStart: 20211213 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1JS8QwGA1uBz2IK-4U9KRUOumS5iiiqKAILsytZCuOS2eYVtF_75cmXVxRwUsZOpPpTF77bfnyHkJbccBIRFPpKp9DghKJ1KUyEK4kCgBnVHUiVopNkLOzuNul51YEMS_lBEiWxc_PdPCvUMM5AFtvnf0F3PWXwgl4DaDDEWCH44-A14ryunyhW68Gumva0MoW_TuV7ZT81Hk7IoVkVHP5aLkPSJzrtYT2wnZT7Rz27kwZOX_oFbVBv9bWvQxHey-P-U27kIDL_hOzldJUt6odLm8aMLUPByNkhDB3lTGSMfFd8PNR24pG1m8aO9gxOizWpeKSVOCjtTaFg9vde6YZoHBg2FODxjXVDYMXljkx1C2v2oeOonFMQgqmeHzv-KB70uyFJZ5liDe_u1rJLnv63l3o81ikFV9czqBpmxg4ewbQWTSisjk0dVqz6ubzaLOC1mmgdfqpU0LrGGgX0NXhweX-kWtFLlyBKSlcTmKPMS6COIqlzykTHJ4RL5QyZqmHFYZ3_VBGqcBRyIiUPgRUUnHOYIAAm7yIxrJ-ppaQA9EkJwHXKT7VEvc09VN4RrknYViHeMvIq_5uIiwDvBYiuU-qVr_bBGYo0TOUeDiBGVpG2_WQgaE_-e7DQTWHiY3fTFyWAOBfD1v527BVNNncxWtorBg-qnU0IZ6KXj7csLfFK5w6ZvA |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Spectral+properties+of+token+graphs&rft.jtitle=Linear+algebra+and+its+applications&rft.au=Barik%2C+Sasmita&rft.au=Verma%2C+Piyush&rft.date=2024-04-15&rft.pub=Elsevier+Inc&rft.issn=0024-3795&rft.eissn=1873-1856&rft.volume=687&rft.spage=181&rft.epage=206&rft_id=info:doi/10.1016%2Fj.laa.2024.02.004&rft.externalDocID=S0024379524000429 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0024-3795&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0024-3795&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0024-3795&client=summon |