A polynomial‐time algorithm for simple undirected graph isomorphism

Summary The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial‐time solution to check if t...

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Vydáno v:	Concurrency and computation Ročník 33; číslo 7; s. 1
Hlavní autoři:	He, Jing, Chen, Jinjun, Huang, Guangyan, Cao, Jie, Zhang, Zhiwang, Zheng, Hui, Zhang, Peng, Zarei, Roozbeh, Sansoto, Ferry, Wang, Ruchuan, Ji, Yimu, Fan, Weibei, Xie, Zhijun, Wang, Xiancheng, Guo, Mengjiao, Chi, Chi‐Hung, Souza, Paulo A., Zhang, Jiekui, Li, Youtao, Chen, Xiaojun, Shi, Yong, Green, David, Kersi, Taraporewalla, Van Zundert, André
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Hoboken Wiley Subscription Services, Inc 10.04.2021
Témata:	Algorithms Arrays equivalence between permutation and bijection graph isomorphism Graphical representations Graphs Isomorphism Mathematical analysis Matrix methods Multiplication Permutations Polynomials polynomial‐time solution reflexivity and duality simple undirected graph Theorems vertex/edge adjacency matrix
ISSN:	1532-0626, 1532-0634
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Abstract	Summary The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial‐time solution to check if two simple undirected graphs are isomorphic or not. Three new representation methods of a graph as vertex/edge adjacency matrix and triple tuple are proposed. A duality of edge and vertex and a reflexivity between vertex adjacency matrix and edge adjacency matrix were first introduced to present the core idea. Beyond this, the mathematical approval is based on an equivalence between permutation and bijection. Because only addition and multiplication operations satisfy the commutative law, we propose a permutation theorem to check fast whether one of two sets of arrays is a permutation of another or not. The permutation theorem was mathematically approved by Integer Factorization Theory, Pythagorean Triples Theorem, and Fundamental Theorem of Arithmetic. For each of two n‐ary arrays, the linear and squared sums of elements were respectively calculated to produce the results.
AbstractList	The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial‐time solution to check if two simple undirected graphs are isomorphic or not. Three new representation methods of a graph as vertex/edge adjacency matrix and triple tuple are proposed. A duality of edge and vertex and a reflexivity between vertex adjacency matrix and edge adjacency matrix were first introduced to present the core idea. Beyond this, the mathematical approval is based on an equivalence between permutation and bijection. Because only addition and multiplication operations satisfy the commutative law, we propose a permutation theorem to check fast whether one of two sets of arrays is a permutation of another or not. The permutation theorem was mathematically approved by Integer Factorization Theory, Pythagorean Triples Theorem, and Fundamental Theorem of Arithmetic. For each of two n‐ary arrays, the linear and squared sums of elements were respectively calculated to produce the results. Summary The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial‐time solution to check if two simple undirected graphs are isomorphic or not. Three new representation methods of a graph as vertex/edge adjacency matrix and triple tuple are proposed. A duality of edge and vertex and a reflexivity between vertex adjacency matrix and edge adjacency matrix were first introduced to present the core idea. Beyond this, the mathematical approval is based on an equivalence between permutation and bijection. Because only addition and multiplication operations satisfy the commutative law, we propose a permutation theorem to check fast whether one of two sets of arrays is a permutation of another or not. The permutation theorem was mathematically approved by Integer Factorization Theory, Pythagorean Triples Theorem, and Fundamental Theorem of Arithmetic. For each of two n‐ary arrays, the linear and squared sums of elements were respectively calculated to produce the results. The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper solves the simple undirected graph isomorphism problem with an algorithmic approach as NP=P and proposes a polynomial‐time solution to check if two simple undirected graphs are isomorphic or not. Three new representation methods of a graph as vertex/edge adjacency matrix and triple tuple are proposed. A duality of edge and vertex and a reflexivity between vertex adjacency matrix and edge adjacency matrix were first introduced to present the core idea. Beyond this, the mathematical approval is based on an equivalence between permutation and bijection. Because only addition and multiplication operations satisfy the commutative law, we propose a permutation theorem to check fast whether one of two sets of arrays is a permutation of another or not. The permutation theorem was mathematically approved by Integer Factorization Theory, Pythagorean Triples Theorem, and Fundamental Theorem of Arithmetic. For each of two n ‐ary arrays, the linear and squared sums of elements were respectively calculated to produce the results.
Author	Zarei, Roozbeh Chen, Xiaojun Zhang, Peng Chi, Chi‐Hung Xie, Zhijun Fan, Weibei Zhang, Jiekui Huang, Guangyan He, Jing Ji, Yimu Shi, Yong Green, David Souza, Paulo A. Van Zundert, André Wang, Xiancheng Cao, Jie Chen, Jinjun Guo, Mengjiao Kersi, Taraporewalla Li, Youtao Zheng, Hui Wang, Ruchuan Zhang, Zhiwang Sansoto, Ferry
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References	1976; 23 2015; 4 2011 1995; 13 2009 2011; 30 1974 2007 2006 1979 1999 1982; 25 2012; 3 2001 1997; 11 2005; 342 2015; 44 2017 2016 2015 2009; 6 1999; 52 1981 2005; 15 1981; 10 e_1_2_10_23_1 Garey MR (e_1_2_10_2_1) 1979 e_1_2_10_24_1 e_1_2_10_21_1 e_1_2_10_22_1 e_1_2_10_20_1 McKay BD (e_1_2_10_18_1) 1981 Balpande V (e_1_2_10_25_1) 2012; 3 Dana‐Picard T (e_1_2_10_6_1) 2009; 6 e_1_2_10_4_1 e_1_2_10_3_1 e_1_2_10_19_1 e_1_2_10_16_1 e_1_2_10_5_1 e_1_2_10_17_1 e_1_2_10_8_1 e_1_2_10_14_1 e_1_2_10_7_1 e_1_2_10_36_1 e_1_2_10_12_1 e_1_2_10_9_1 e_1_2_10_13_1 e_1_2_10_34_1 e_1_2_10_10_1 e_1_2_10_11_1 e_1_2_10_32_1 e_1_2_10_31_1 e_1_2_10_30_1 Aho AV (e_1_2_10_15_1) 1974 Silverman JH (e_1_2_10_35_1) 2006 Balpande V (e_1_2_10_26_1) 2015; 4 e_1_2_10_29_1 Wussing H (e_1_2_10_33_1) 2007 e_1_2_10_27_1 e_1_2_10_28_1
References_xml	– year: 2011 – year: 2009 – year: 1981 – volume: 23 start-page: 433 issue: 3 year: 1976 end-page: 445 article-title: A fast backtracking algorithm to test directed graphs for isomorphism using distance matrices publication-title: J ACM – year: 2001 – year: 2007 – volume: 44 start-page: 114 issue: 1 year: 2015 end-page: 159 article-title: Structure theorem and isomorphism test for graphs with excluded topological subgraphs publication-title: SIAM J Comput – year: 2015 article-title: Mathematician claims breakthrough in complexity theory publication-title: Science News – volume: 6 start-page: 477 issue: 3 year: 2009 end-page: 494 article-title: Graph isomorphisms and matrix similarity: switching between representations publication-title: Math Enthus – year: 1979 – volume: 342 start-page: 657 issue: 6 year: 2005 end-page: 673 article-title: Some further development on the eigensystem approach for graph isomorphism detection publication-title: J Franklin Inst – year: 2016 – volume: 3 issue: 6 year: 2012 article-title: Graph invariants and graph isomorphism publication-title: IJCTA – volume: 10 start-page: 203 issue: 1 year: 1981 end-page: 225 article-title: Linear time automorphism algorithms for trees, interval graphs, and planar graphs publication-title: SIAM J Comput – volume: 15 start-page: 181 issue: 2 year: 2005 end-page: 184 article-title: Algorithm of graph isomorphism with three dimensional DNA graph structures publication-title: Prog Nat Sci – volume: 30 start-page: 1115 issue: 5 year: 2011 end-page: 1130 article-title: A new algorithm for isomorphism determination of undirected graphs‐circuit simulation method publication-title: Circuits Syst Signal Process – volume: 13 start-page: 45 issue: 1 year: 1995 end-page: 60 article-title: Pattern recognition by homomorphic graph matching using Hopfield neural networks publication-title: Image Vis Comput – year: 2006 – year: 1974 – volume: 11 start-page: 169 issue: 01 year: 1997 end-page: 203 article-title: Recent advances in graph matching publication-title: Int J Pattern Recognit Artif Intell – volume: 4 start-page: 1 issue: 4 year: 2015 end-page: 5 article-title: An approach of graph isomorphism detection based on vertex‐invariant publication-title: Int J Adv Stud Comput Sci Eng – year: 2017 – volume: 25 start-page: 42 issue: 1 year: 1982 end-page: 65 article-title: Isomorphism of graphs of bounded valence can be tested in polynomial time publication-title: J Comput Syst Sci – year: 2015 – year: 1999 – volume: 52 start-page: 143 issue: 1‐3 year: 1999 end-page: 153 article-title: Three dimensional DNA structures in computing publication-title: Biosystems – ident: e_1_2_10_19_1 doi: 10.1007/978-3-642-02011-7_21 – ident: e_1_2_10_28_1 doi: 10.1016/S0303-2647(99)00041-6 – ident: e_1_2_10_5_1 – ident: e_1_2_10_30_1 – ident: e_1_2_10_13_1 – ident: e_1_2_10_3_1 doi: 10.1126/science.aad7416 – ident: e_1_2_10_36_1 – ident: e_1_2_10_9_1 doi: 10.1007/s00034-010-9248-7 – ident: e_1_2_10_12_1 doi: 10.1145/2815400.2815410 – ident: e_1_2_10_32_1 – volume-title: Practical Graph Isomorphism year: 1981 ident: e_1_2_10_18_1 – ident: e_1_2_10_21_1 – volume: 3 issue: 6 year: 2012 ident: e_1_2_10_25_1 article-title: Graph invariants and graph isomorphism publication-title: IJCTA – ident: e_1_2_10_8_1 doi: 10.1016/j.jfranklin.2005.04.006 – volume-title: The Genesis of the Abstract Group Concept: A Contribution to the History of the Origin of Abstract Group Theory year: 2007 ident: e_1_2_10_33_1 – ident: e_1_2_10_24_1 – volume-title: Computers and Intractability: A Guide to the Theory of np‐Completeness year: 1979 ident: e_1_2_10_2_1 – volume: 4 start-page: 1 issue: 4 year: 2015 ident: e_1_2_10_26_1 article-title: An approach of graph isomorphism detection based on vertex‐invariant publication-title: Int J Adv Stud Comput Sci Eng – ident: e_1_2_10_10_1 doi: 10.1109/IEOM.2015.7093815 – ident: e_1_2_10_20_1 – volume: 6 start-page: 477 issue: 3 year: 2009 ident: e_1_2_10_6_1 article-title: Graph isomorphisms and matrix similarity: switching between representations publication-title: Math Enthus doi: 10.54870/1551-3440.1166 – ident: e_1_2_10_14_1 doi: 10.1145/800119.803896 – ident: e_1_2_10_34_1 – ident: e_1_2_10_7_1 doi: 10.1137/120892234 – ident: e_1_2_10_17_1 doi: 10.1016/0022-0000(82)90009-5 – ident: e_1_2_10_31_1 – ident: e_1_2_10_27_1 doi: 10.1080/10020070512331341960 – ident: e_1_2_10_16_1 doi: 10.1137/0210015 – ident: e_1_2_10_22_1 doi: 10.1142/S0218001497000081 – ident: e_1_2_10_11_1 doi: 10.1016/0262-8856(95)91467-R – ident: e_1_2_10_4_1 – volume-title: A Friendly Introduction to Number Theory year: 2006 ident: e_1_2_10_35_1 – ident: e_1_2_10_29_1 doi: 10.1145/2897518.2897542 – volume-title: The Design and Analysis of Computer Algorithms year: 1974 ident: e_1_2_10_15_1 – ident: e_1_2_10_23_1 doi: 10.1145/321958.321963
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Snippet	Summary The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper... The graph isomorphism problem is to determine two finite graphs that are isomorphic which is not known with a polynomial‐time solution. This paper solves the...
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SubjectTerms	Algorithms Arrays equivalence between permutation and bijection graph isomorphism Graphical representations Graphs Isomorphism Mathematical analysis Matrix methods Multiplication Permutations Polynomials polynomial‐time solution reflexivity and duality simple undirected graph Theorems vertex/edge adjacency matrix
Title	A polynomial‐time algorithm for simple undirected graph isomorphism
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