1998
DOI: 10.1021/ci9702914
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Isomorphism, Automorphism Partitioning, and Canonical Labeling Can Be Solved in Polynomial-Time for Molecular Graphs

Abstract: The graph isomorphism problem belongs to the class of NP problems, and has been conjectured intractable, although probably not NP-complete. However, in the context of chemistry, because molecules are a restricted class of graphs, the problem of graph isomorphism can be solved efficiently (i.e., in polynomial-time). This paper presents the theoretical results that for all molecules, the problems of isomorphism, automorphism partitioning, and canonical labeling are polynomial-time problems. Simple polynomial-tim… Show more

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Cited by 61 publications
(74 citation statements)
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“…For chemical subgraph searches this time-consuming step at best runs in polynomial time. 16 To speed up the process we apply a two-step procedure of a fingerprint based prescreening followed by a full subgraph matching in the screening result. Fingerprints are one-dimensional bit arrays, where bits are set according to the occurrence of a particular structural feature.…”
Section: User-defined Database Functions Specific To Chemistrymentioning
confidence: 99%
“…For chemical subgraph searches this time-consuming step at best runs in polynomial time. 16 To speed up the process we apply a two-step procedure of a fingerprint based prescreening followed by a full subgraph matching in the screening result. Fingerprints are one-dimensional bit arrays, where bits are set according to the occurrence of a particular structural feature.…”
Section: User-defined Database Functions Specific To Chemistrymentioning
confidence: 99%
“…The first is the Moscow school around Academician Nikolai Serafimovich Zefirov, that includes Drs Palyulin, Skvortsova, and Baskin [49][50][51][52][53][54][55][56][57][58][59][60]. Another remarkable group is around Dr Jean-Loup Faulon [61][62][63][64][65][66][67][68]. Professors Lemont B. Kier and Lowell H. Hall have published several papers on this topic [69][70][71].…”
Section: Triplet and Kier-hall Indices With Very Low Degeneracy Corrementioning
confidence: 99%
“…In the graphical method of representation, the reaction rules take the form of graph rewriting rules, with subgraphs replacing the regular expressions of BioNetGen. This new approach to model specification is inspired by the use of graphs and graph rewriting rules to model chemical systems (for examples, see [21,22,[71][72][73][74]). The literature about the use of rules, including graph rewriting rules, to model systems is substantial.…”
Section: Discussionmentioning
confidence: 99%