On the spectral radius and energy of the weighted adjacency matrix of a graph

Baogen Xu, Shuchao Li, Rong Yu and Qin Zhao

Applied Mathematics and Computation, 2019, vol. 340, issue C, 156-163

Abstract: Let G be a graph of order n and let di be the degree of the vertex vi in G for i=1,2,…,n. The weighted adjacency matrix Adb of G is defined so that its (i, j)-entry is equal to di+djdidj if the vertices vi and vj are adjacent, and 0 otherwise. The spectral radius ϱ1 and the energy Edb of the Adb-matrix are examined. Lower and upper bounds on ϱ1 and Edb are obtained, and the respective extremal graphs are characterized.

Keywords: Weighted adjacency matrix; Weighted spectral radius; Weighted energy (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:340:y:2019:i:c:p:156-163

DOI: 10.1016/j.amc.2018.08.012

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