Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Distance Eccentric Connectivity Index of Graphs

  • Alqesmah, Akram (Department of Studies in Mathematics, University of Mysore) ;
  • Saleh, Anwar (Department of Mathematics, Faculty of Science, University of Jeddah) ;
  • Rangarajan, R. (Department of Studies in Mathematics, University of Mysore) ;
  • Gunes, Aysun Yurttas (Bursa Uludag University) ;
  • Cangul, Ismail Naci (Bursa Uludag University)
  • Received : 2019.07.06
  • Accepted : 2020.05.18
  • Published : 2021.03.31
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Abstract

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

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