循环图C2n(1,n-1)的临界群  

The critical group of Cyclic Graph C2n(1,n-1)

作　　者：王倩南 侯耀平 WANG Qiannan;HOU Yaoping(School of Mathematics and Statistics,Hunan Normal University,Changsha 410000,China)

机构地区：[1]湖南师范大学数学与统计学院,湖南长沙410000

出　　处：《邵阳学院学报（自然科学版）》2020年第2期13-22,共10页Journal of Shaoyang University：Natural Science Edition

基　　金：湖南省自然科学基金(2019JJ40184)。

摘　　要：连通图的临界群是阶数为生成树数目的有限阿贝尔群,连通图生成树的数目与Laplacian矩阵有关,可以用矩阵树定理求得。文中给出了循环图C2n(1,n-1)的临界群的代数结构,它是n个或n+1个循环群的直和。The critical groups of connected graphs are finite Abelian groups whose order is the number of spanning trees corresponding to the connected graph.In fact,the number of spanning trees is connected to the Laplacian matrix of graph,which is obtained by the Matrix-tree Theorem.In this paper,the critical groups of cyclic graph C2n(1,n-1)were studied and the algebraic structure of the critical group which is the direct sum of n or n+1 cyclic group was presented.

关 键 词：循环图 LAPLACIAN矩阵 Smith标准型 临界群 

分 类 号：O157.6[理学—数学]