Spectral properties with the difference between topological indices in graphs
type: Item
instance of: scholarly article
title: Spectral properties with the difference between topological indices in graphs
zbMATH Open document ID: 1489.05023
DOI: 10.1155/2020/6973078
author: Akbar Jahanbani
author: Roslan Hasni
author: Zhibin Du
author: Seyed Mahmood Sheikholeslami
published in: Journal of Mathematics
publication date: 2021-01-07T00:00:00Z
review text: Summary: Let \(G\) be a graph of order \(n\) with vertices labeled as \(v_1, v_2,\dots, v_n\). Let \(d_i\) be the degree of the vertex \(v_i\), for \(i=1,2,\dots,n\). The difference adjacency matrix of \(G\) is the square matrix of order \(n\) whose \((i,j)\) entry is equal to \((\sqrt{ d_i + d_j - 2} - 1)/( \sqrt{d_i d_j})\) if the vertices \(v_i\) and \(v_j\) of \(G\) are adjacent or \((v_i v_j \in E (G))\) and zero otherwise. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix, that is, a modification of the classical adjacency matrix involving the degrees of the vertices. In this paper, some properties of its characteristic polynomial are studied. We also investigate the difference energy of a graph. In addition, we establish some upper and lower bounds for this new energy of graph.
Mathematics Subject Classification ID: 05C09
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 7290898
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/6973078
OpenAlex ID: W3044211576
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description: scientific article; zbMATH DE number 7290898