On the spectral moment of quasi-bicyclic graphs

摘要

Let G be a connected graph. If G contains a vertex v such that G−v is a bicyclic graph, then G is called a quasi-bicyclic graph. Let Bn,d¯={G : G is a quasi-bicyclic graph of order n with G−u¯ being bicyclic and dG(u¯)=d¯}. We study structure characteristics of graphs on spectral moments. We also determine the last and the second last quasi-bicyclic graphs, in S-order, among all graphs in Bn,d¯, respectively.