On the eigenvalue and energy of extended adjacency matrix

The extended adjacency matrix of graph G, A(ex) is a symmetric real matrix that if i not equal j and u(i)u(j) is an element of E(G), then the ijth entry is d(ui)(2) + d(uj)(2)/2d(ui)d(uj), and zero otherwise, where d(u), indicates the degree of vertex u. In the present paper, several investigations of the extended adjacency matrix are undertaken and then some spectral properties of A(ex) are given. Moreover, we present some lower and upper bounds on extended adjacency spectral radii of graphs. Besides, we also study the behavior of the extended adjacency energy of a graph G. (C) 2020 Published by Elsevier Inc.

Automated summary

This paper investigates the extended adjacency matrix of a graph, explores its spectral properties and provides lower and upper bounds on the extended adjacency spectral radii. Additionally, the behavior of the extended adjacency energy of the graph is studied.