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On the eigenvalue and energy of extended adjacency matrix

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  • Ghorbani, Modjtaba
  • Li, Xueliang
  • Zangi, Samaneh
  • Amraei, Najaf

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.

Suggested Citation

  • Ghorbani, Modjtaba & Li, Xueliang & Zangi, Samaneh & Amraei, Najaf, 2021. "On the eigenvalue and energy of extended adjacency matrix," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300320308924
    DOI: 10.1016/j.amc.2020.125939
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    References listed on IDEAS

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    1. Das, Kinkar Ch. & Gutman, Ivan & Furtula, Boris, 2017. "On spectral radius and energy of extended adjacency matrix of graphs," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 116-123.
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    Cited by:

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