Graphs Whose Critical Groups Have Larger Rank 被引量：3

Graphs Whose Critical Groups Have Larger Rank

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摘要 The critical group C（G） of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r（G） be the minimum number of generators （i.e., the rank） of the group C（G） and β（G） be the number of independent cycles of G. In this paper, some forbidden induced subgraphs axe given for r（G） = n - 3 and all graphs with r（G） = j3（G） = n - 3 are characterized The critical group C（G） of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r（G） be the minimum number of generators （i.e., the rank） of the group C（G） and β（G） be the number of independent cycles of G. In this paper, some forbidden induced subgraphs axe given for r（G） = n - 3 and all graphs with r（G） = j3（G） = n - 3 are characterized

作者 Yao Ping HOU Wai Chee SHIU Wai Hong CHAN

机构地区 Departement of Mathematics Department of Mathematics

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第9期1663-1670,共8页 数学学报（英文版）

基金 Supported by FRG, Hong Kong Baptist-University the first author is supported by National Natural Science Foundation of China （Grant No. 10671061） The authors would like to thank the anonymous referee for a number of helpful suggestions.

关键词 Critical group of a graph Laplacian matrix Smith normal form Critical group of a graph, Laplacian matrix, Smith normal form

分类号 O157.5 [理学—基础数学] TP391.41 [自动化与计算机技术—计算机应用技术]

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参考文献9

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Acta Mathematica Sinica,English Series

2011年第9期

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Graphs Whose Critical Groups Have Larger Rank 被引量：3

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