一类单圈图的Laplacian谱刻画

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.%It is difficult to determine which graphs can be determined by their spectra.Based on lollipop graph and graph H(n;q,n1,n2),a new family of graphs was defined and denoted by H(n;q,n1,n2,n3),which was a graph of order n obtained by attaching three hanging paths Pn1,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.