图的Resolvent Estrada指标的上(下)界刻画

Description of the upper(lower) bounds of Resolvent Estrada index

图G的Resolvent Estrada指标是Estrada和Higham在2010年提出的用于检测复杂网络和分子结构中心度的一类重要的图的拓扑指标,其定义为REE(G)=n∑i=1(n-1/n-1-λi)=n∑i=1(1-λ1/n-1_^-1其中λ1,λ2,…,λn表示图G的邻接矩阵的特征值。该指标经常用于量化分子链的度,因此在量子化学领域存在广泛的应用。本文使用柯西-施瓦兹等不等式和Resolvent Estrada能量来刻画Resolvent Estrada指标的若干上界和下界。

The Resolvent Estrada index in graph G is the topological index of a class of important graphs proposed by Estrada and Higham in 2010 to detect the centrality of complex networks and molecular structures. It is defined as follow. REE(G)=n∑i=1(n-1/n-1-λi)=n∑i=1(1-λ1/n-1_^-1where λ1,λ2,…,λn are the eigenvalues of the adjacency matrix of G. REE(G) is often used to quantify the degree of molecular chains so that it is widely used in the filed of the quantum chemistry. In this paper, Cauchy-Schwartz inequality and Resolvent Estrada energy are used to describe the upper and lower bounds of Resolvent Estrada index.