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Remark on spectral study of the geometric–arithmetic index and some generalizations

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  • Milovanović, E.I.
  • Milovanović, I.Ž.
  • Matejić, M.M.

Abstract

Let G=(V,E),V={1,2,…,n}, be a simple connected graph with n vertices, m edges, and sequence of vertex degrees d1 ≥ d2 ≥ ⋅⋅⋅ ≥ dn > 0, di=d(i). A large number of vertex–degree-based topological indices is of the form TI=TI(G)=∑i∼jF(di,dj), where F is pertinently chosen function with the property F(x,y)=F(y,x). To each of such topological indices a corresponding adjacency matrix A=(aij), of order n × n, can be associated. The trace of matrix A is denoted as tr(A). For F(di,dj)=2didjdi+dj, the geometric–arithmetic topological index, GA1, is obtained. Upper and lower bounds for GA1 in terms of tr(A2) are determined. Also, we generalize a number of results reported in the literature and obtain some new bounds for the indices of the form TI.

Suggested Citation

  • Milovanović, E.I. & Milovanović, I.Ž. & Matejić, M.M., 2018. "Remark on spectral study of the geometric–arithmetic index and some generalizations," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 206-213.
    • Handle: RePEc:eee:apmaco:v:334:y:2018:i:c:p:206-213
    DOI: 10.1016/j.amc.2018.04.006
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    References listed on IDEAS

    as
    1. Rodríguez, José M. & Sigarreta, José M., 2016. "Spectral properties of geometric–arithmetic index," Applied Mathematics and Computation, Elsevier, vol. 277(C), pages 142-153.
    2. Tsang, Eric W. K., 2014. "Old and New," Management and Organization Review, Cambridge University Press, vol. 10(03), pages 390-390, November.
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    Cited by:

    1. Yu Yang & Long Li & Wenhu Wang & Hua Wang, 2020. "On BC-Subtrees in Multi-Fan and Multi-Wheel Graphs," Mathematics, MDPI, vol. 9(1), pages 1-29, December.

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