On the incidence Estrada index of graphs
type: Item
instance of: scholarly article
zbMATH Open document ID: 1344.05091
author: Wu-xin Liu
author: Fuyi Wei
publication date: 2016-06-10T00:00:00Z
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C07
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 6592397
zbMATH Keywords: signless Laplacian matrix
zbMATH Keywords: incidence energy
zbMATH Keywords: Estrada index
zbMATH Keywords: Nordhaus-Gaddum inequality
MaRDI profile type: Publication
title: On the incidence Estrada index of graphs
published in: Utilitas Mathematica
review text: Let \(A\) and \(D\) be the adjacency matrix and the diagonal matrix of vertex degrees of a graph \(G\). The matrix \(Q=D+A\) is called the signless Laplacian matrix of \(G\) (in analogy to the combinatorial Laplacian matrix \(D-A\)). Let \(\mu_1,\dots,\mu_n\) be the eigenvalues of \(Q\). The authors study the graph invariant \(\sum_{i=1}^n e^{\sqrt{\mu_i}}\), which is named the incidence Estrada index here, and give a few lower and upper bounds for it in terms of the numbers of vertices, edges and \(\sum_{i=1} \sqrt{\mu_i}\).
reviewed by: Dragan Stevanović
description: scientific article; zbMATH DE number 6592397