一些具有较多边数图的临界群

journal6 ›› 2005, Vol. 26 ›› Issue (4): 84-88.

一些具有较多边数图的临界群

(1.邵阳广播电视大学，湖南邵阳 422000;2.湖南师范大学数学系，湖南长沙 410081)

出版日期:2005-10-15 发布日期:2012-09-17
作者简介:徐幼专(1971-)，女，湖南省新邵县人，湖南师大数学系硕士研究生，邵阳广播电视大学讲师，主要从事基础数学研究.
基金资助:
湖南省教育厅科学研究资助项目(03B019)

Critical Groups For Some Graphs With Large Number of Edges

(1.Shaoyang Radio Television University,Shaoyang 422000,Hunan China;2.Department of Mathematics,Hunan Normal University,Changsha 410081,Hunan China)

Online:2005-10-15 Published:2012-09-17

摘要/Abstract

摘要：图的临界群是图生成树数目的一个加细，图的临界群的阶数恰为该图的生成树的数目.确定了一些具有较多边数图如Kn-K1，m，Kn-Km，Kn-mK2，Kn，n-nK2的临界群的结构，证明了这些图的临界群不是一个循环群，而是多个循环群的直和.

关键词： 图的Laplacian矩阵, 临界群, 群的Smith标准形

Abstract: The critical group of a connected graph is a finite abelian group whose order is the number of spanning trees in the graph and is closely related to the graph Laplacian.In this paper,the critical groups for some graphs with large number of edges,such as Kn-K1，m，Kn-Km，Kn-mK2，Kn，n-nK2,are determined completely.

Key words: graph laplacian, critical group, the Smith normal form

徐幼专, 侯耀平. 一些具有较多边数图的临界群[J]. journal6, 2005, 26(4): 84-88.

XU You-Zhuan, HOU Yao-Ping. Critical Groups For Some Graphs With Large Number of Edges[J]. journal6, 2005, 26(4): 84-88.