On the eigenvalue and energy of extended adjacency matrix

Modjtaba Ghorbani, Xueliang Li, Samaneh Zangi and Najaf Amraei

Applied Mathematics and Computation, 2021, vol. 397, issue C

Abstract: The extended adjacency matrix of graph G,Aex is a symmetric real matrix that if i≠j and uiuj∈E(G), then the ijth entry is dui2+duj2/2duiduj, and zero otherwise, where du 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 Aex 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.

Keywords: Extended adjacency matrix; Graph eigenvalue; Graph energy (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308924

DOI: 10.1016/j.amc.2020.125939

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