路图与圈图的积图的临界群  

The Critical Group of Graph P_m and C_n

作　　者：陈平鸽[1] 侯耀平[1] 

机构地区：[1]湖南师范大学数学系,湖南长沙410081

出　　处：《湖南工业大学学报》2008年第2期21-24,共4页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(10471037);湖南省教育厅科研基金资助项目(06A037)

摘　　要：图的临界群是图生成树数目的一个加细。确定了积图Pm.Cn(m≤4)的临界群的结构,证明了P3.Cn的临界群恰好为n+1个偶数阶循环群的直和,而P4.Cn的临界群恰好为3个偶数阶循环群的直和。We study the structure of the critical group on the graph Pm· Cn （ m≤4 ）, An explicit expression of the Smith normal form of critical group on the graph P3·Cn and P4· Cn can be decided, which are always the direct product of n＋1 cyclic groups with even order and the direct product of three cyclic groups with even order respectively.

关 键 词：图的Laplacian矩阵 临界群 群的Smith标准形 路 圈 

分 类 号：O157.5[理学—数学]