一类单圈图的Laplacian谱刻画

Characterizing some class of unicyclic graph by its Laplacian spectrum

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.