Description of the upper(lower)bounds of Resolvent Estrada index
- JIA Shu-xiang, DENG Bo, YE Cheng-fu, FU Feng, CHEN Hui-long
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(4):
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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)=∑ni=1((n-1)/(n-1-λi))=∑ni=1(1-(λ1)/(n-1))-1,where 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.