摘要
图的临界群是图生成树数目的一个加细.它是图的一个精细不变量,与图的Laplacian矩阵密切相关.将冠图分为点冠图和边冠图,通过在整数环Z上实施一系列的行列变换来计算整数矩阵的Smith标准型,从而确定了点冠图Tm○Pn和边冠图Tm◇Pn的临界群的代数结构.进一步,证明了点冠图Tm○Pn和边冠图Tm◇Pn的临界群的Smith标准型分别为m和2(m-1)个循环群的直和,同时给出了图Tm○Pn和Tm◇Pn的生成树数目.
The critical group of a graph is a refinement of the number of spanning trees of the graph.It is a subtle isomorphism invariant of a graph and is closely connected with the graph Laplacian matrix.The corona of a graph is divided into the vertex corona and the edge corona.Through the implementation of a series of row and column operations in the ring Z of integers,the Smith normal form of an integer matrix is obtained.Hence,the structures of the critical group on the vertex corona Tm○Pn and the edge corona Tm◇Pn are determined.Furthermore,it is proved that the Smith normal forms of critical group of Tm○Pn and Tm◇Pn are the direct sum of m and 2（m-1） cyclic groups,respectively.At the same time the number of spanning trees in Tm○Pn and Tm◇Pn are also given.
出处
《晓庄学院自然科学学报》
CAS
北大核心
2012年第3期10-15,共6页
Journal of Natural Science of Hunan Normal University
基金
国家科技支撑计划资助项目(2009BAG13A06)
江苏省普通高校研究生科研创新计划资助项目(CX22-0163)
东南大学优秀博士论文基金资助项目(YBJJ1140)
