图P_n×C_3的临界群  

On the Critical Group of Graph P_n×C_3

作　　者：陈平鸽[1] 侯耀平[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,中国长沙410081

出　　处：《湖南师范大学自然科学学报》2005年第4期5-7,16,共4页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金(10471037);湖南省教育厅科学研究资助项目(03B019)

摘　　要：图的临界群是图生成树数目的一个加细.它是定义在图上的一个有限交换群,其群结构是图的一个精细不变量,与图的Laplacian理论密切相关.确定了Pn×C3的临界群的结构,证明了Pn×C3的临界群同构于Ztn Z3tn,其中tn满足递推关系tn=5tn-1-tn-2,n≥2及t0=0,t1=1.从而K(Pn×C3)恰为两个循环群的直和.The critical group of a connected graph is a finite abelian group whose structure is a subtle isomorphism invariant of the graph. It is closely connected with Laplacian theory of graph. The structure of the critical group on graph Pn×C3 is studied. An explicit expression of the Smith normal form of critical group on graph Pn×C3 is given, which is isomorphic to Zrn＋Z3tn, where to tn=5tn-1-ln-2,n≥2 and to=0,t1=1. So K（Pn×C3 ） is the direct product of two cyclic groups.

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

分 类 号：O157.5[理学—数学]