一类单圈图的Laplacian谱刻画  

Characterizing some class of unicyclic graph by its Laplacian spectrum

作　　者：卢鹏丽[1] 王旭柱[1] 陈作汉[1] 

机构地区：[1]兰州理工大学计算机与通信学院,甘肃兰州730050

出　　处：《哈尔滨工程大学学报》2012年第7期851-854,共4页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(61064011);兰州理工大学校基金资助项目(0914ZX136)

摘　　要：针对哪些图可由它们的谱刻画这一问题,在lollipop图和图H(n;q,n1,n2)的基础上定义了一类新的图类,符号表示为H(n;q,n1,n2,n3),它是通过在圈Cq的同一个顶点上连接3条悬挂路Pn1、Pn2、Pn3而得到的顶点数为n的单圈图.首先,证明了此图类中,如果2个图形不同构,那么它们必定具有不同的Laplacian谱.在此结论的基础上,证明了图H(n;q,n1,n2,n3)可由它的Laplacian谱刻画.h is difficult to determine which graphs can be determined by their spectra. Based on lollipop graph and graph H（ n ;q, nl, n2 ）, a new family of graphs of order n obtained by attaching three hanging was defined and denoted by H（n ;q, hi, n2, n3 ）, which was a graph paths Pox, Pn2 and Pn3 at the same vertex of cycle Cq. First, it was proven that if two graphs in the family of the graphs are non-isomorphic, they must have different Laplacian spectra. Then, it was proven that the graph H（ n ; q, n1, n2, n3 ） is determined by its Laplacian spectrum.

关 键 词：LAPLACIAN矩阵 Laplacian特征多项式 L-同谱 L-谱 

分 类 号：O157[理学—数学]