Graphs Whose Critical Groups Have Larger Rank  

作　　者：Yao Ping HOU Wai Chee SHIU Wai Hong CHAN 

机构地区：[1]Departement of Mathematics, Hu'nan Normal University, Changsha 410081, P. R. China [2]Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》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.

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 characterizedThe 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

关 键 词：Critical group of a graph Laplacian matrix Smith normal form 

分 类 号：O157.5[理学—数学] TP391.41[理学—基础数学]