2-连通三圈图的零化度

On the Nullity of 2-Connected Tricycle Graphs

本文所考虑的图均为无向简单图.图G的特征多项式的根称为图G的特征值,也构成图G的谱.图G的谱中零根的个数称为该图的零化度,记为η(G).设Gn表示所有顶点数为n的图的集合,[0,n]=0,1,2,…,n,非空子集N∈[0,n].若对k∈N,都■G∈Gn,使得η(G)=k,则N称为Gn的零化集.本文主要研究2-连通三圈图的零化度.

The graphs in this paper are simple undirected graphs. The roots of characteristic polynomial of graph G are called the eigenvalues of G, and also form the spectrum of the graph. The number of zero eigenvalues in the spectrum of the graph G is called its nullity, and is denoted by η（G）. Let Gn be the set of all graphs of order n,and let [0,n] =0,1, 2,... ,n. A subset N of [0 ,n] is said to be the nullity set of Gn provided that for any k∈N,there exists at least one graph G∈Gn such that η（G） =k. In this paper we discuss the nullity of 2 -connected tricycle graphs.