Estrada指数的极小树

The Minimum Estrada Index of Trees

设G为一个n阶图,G的邻接矩阵A(G)的特征值为λ1,λ2,…,λn,Estrada指数被定义为EE(G)=Σni=1eλi。该文确定了如下树类中Estrada指数的极小图,此类中的树均有n个顶点且恰好包含有两个最大度为△的顶点。进一步提出了一个关于如下树类中Estrada指数的极小图的猜想,此类中的树均有n个顶点且恰好包含有k个最大度为△的顶点。

Let be a graph of order,and letλ1,λ2,…,λn be the eigenvalues of the adjacency matrix of.The Estrada index is defined as Σni = 1 eλi.In this paper,we determine the unique tree with minimum Estrada index among the trees on vertices with two vertices of maximum degree equal to.Furthermore,we present a conjecture about the unique tree with minimum Estrada index among the trees on vertices containing exactly vertices of maximum degree equal to.