On the spectral moment of quasi-bicyclic graphs
Abstract 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 B n , d ¯ = { G : G is a quasi-bicyclic graph of order n with G − u ¯ being bicyclic and d G ( 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 B n , d ¯ , respectively.