刊名:Journal of Mathematical Analysis and Applications
出版年:2016
出版时间:15 April 2016
年:2016
卷:436
期:2
页码:1242-1255
全文大小:487 K
文摘
Let be the set of all connected bipartite bicyclic graphs with n vertices. The Estrada index of a graph G is defined as , where λ1,λ2,…,λn are the eigenvalues of the adjacency matrix of G, and the Kirchhoff index of a graph G is defined as Kf(G)=∑i<jrij, where rij is the resistance distance between vertices vi and vj in G. The complement of G is denoted by . In this paper, sharp upper bound on EE(G) (resp. ) of graph G in is established. The corresponding extremal graphs are determined, respectively. Furthermore, by means of some newly created inequalities, the graph G in with the second maximal EE(G) (resp. ) is identified as well. It is interesting to see that the first two bicyclic graphs in according to these two orderings are mainly coincident.