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

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  • Shao, Yanling
  • Gao, Yubin

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.

Suggested Citation

  • Shao, Yanling & Gao, Yubin, 2019. "The maximal geometric-arithmetic energy of trees with at most two branched vertices," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    • Handle: RePEc:eee:apmaco:v:362:y:2019:i:c:13
    DOI: 10.1016/j.amc.2019.06.042
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    References listed on IDEAS

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    1. Monsalve, Juan & Rada, Juan & Shi, Yongtang, 2019. "Extremal values of energy over oriented bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 26-34.
    2. Rodríguez, José M. & Sigarreta, José M., 2016. "Spectral properties of geometric–arithmetic index," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 142-153.
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