Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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SOME INEQUALITIES FOR GENERAL SUM-CONNECTIVITY INDEX

  • MATEJIC, M.M. (Department of Mathematics, Faculty of Electronic Engineering, University of Nis) ;
  • MILOVANOVIC, I.Z. (Department of Mathematics, Faculty of Electronic Engineering, University of Nis) ;
  • MILOVANOVIC, E.I. (Department of Computer Science, Faculty of Electronic Engineering, University of Nis)
  • Received : 2019.06.19
  • Accepted : 2020.01.10
  • Published : 2020.01.30
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Abstract

Let G be a simple connected graph with n vertices and m edges. Denote by d1 ≥ d2 ≥ ⋯ ≥ dn > 0 and d(e1) ≥ d(e2) ≥ ⋯ ≥ d(em) sequences of vertex and edge degrees, respectively. If vertices vi and vj are adjacent, we write i ~ j. The general sum-connectivity index is defined as 𝒳α(G) = ∑i~j(di + dj)α, where α is an arbitrary real number. Firstly, we determine a relation between 𝒳α(G) and 𝒳α-1(G). Then we use it to obtain some new bounds for 𝒳α(G).

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