The maximal geometric-arithmetic energy of trees with at most two branched vertices

Yanling Shao and Yubin Gao

Applied Mathematics and Computation, 2019, vol. 362, issue C, -

Abstract: Let G be a graph of order n with vertex set V(G)={v1,v2,…,vn} and edge set E(G), and d(vi) be the degree of the vertex vi. The geometric-arithmetic matrix of G, recently introduced by Rodríguez and Sigarreta, is the square matrix of order n whose (i, j)-entry is equal to 2d(vi)d(vj)d(vi)+d(vj) if vivj ∈ E(G), and 0 otherwise. The geometric-arithmetic energy of G is the sum of the absolute values of the eigenvalues of geometric-arithmetic matrix of G. In this paper, we characterize the tree of order n which has the maximal geometric-arithmetic energy among all trees of order n with at most two branched vertices.

Keywords: Tree; Geometric-arithmetic index; Geometric-arithmetic energy (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:362:y:2019:i:c:13

DOI: 10.1016/j.amc.2019.06.042

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