双圈图的最大Estrada指数

Bicyclic graph with the maximal Estrada indices

令B_n^+表示顶点个数为n的双圈二部图的集合.考虑了B_n^+中图依Estrada指数从大到小的排序问题.利用二部图的Estrada指数和最大特征值之间的关系,当n≥8时,得到了B_n^+中具有最大和次大Estrada指数的图.

Let Bn^＋ be the set of bipartite bicyclic graphs with n vertices. In Bn^＋ ordering the graphs in terms of their maximal Estrada indices was considered. With the aid of a relationship between the Estrada index and the largest eigenvalue of the bipartite graphs, we deduce the graphs with the largest and the second largest Estrada indices in Bn^＋ for n ≥8.