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eISSN 0454-8124
pISSN 1225-6951

### Article

Kyungpook Mathematical Journal 2021; 61(1): 61-74

Published online March 31, 2021

### Distance Eccentric Connectivity Index of Graphs

Akram Alqesmah, Anwar Saleh, R. Rangarajan, Aysun Yurttas Gunes and Ismail Naci Cangul∗

Department of Studies in Mathematics, University of Mysore, Mysore 570006, India
e-mail: aalqesmah@gmail.com

Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
e-mail: asaleh1@uj.edu.sa

Department of Studies in Mathematics, University of Mysore, Mysore 570006, India
e-mail: rajra63@gmail.com

Bursa Uludag University, Mathematics, Gorukle 16059 Bursa-Turkey
e-mail: ayurttas@uludag.edu.tr and cangul@uludag.edu.tr

Received: July 6, 2019; Revised: April 14, 2020; Accepted: May 18, 2020

### Abstract

Let $G=(V,E)$ be a connected graph. The eccentric connectivity index of G is defined by $ξC(G)=∑ u∈V(G)deg(u)e(u)$, 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 $ξC$ that will be called the distance eccentric connectivity index of G and defined by $ξDe(G)=∑ u∈V(G)degDe(u)e(u)$ 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.

Keywords: eccentric connectivity index, distance eccentric connectivity index, topological graph index, graph operation.