**Journal of Prime Research in Mathematics**

Vol. 14 (2018), Issue 1, pp. 87 – 99

ISSN: 1817-3462 (Online) 1818-5495 (Print)

ISSN: 1817-3462 (Online) 1818-5495 (Print)

**Connective eccentricity index of certain path-thorn graphs**

**M. Javaid
**Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan.

**Department of Mathematics, School of Science, University of Management and Technology, Lahore, Pakistan.**

M. Ibraheem

M. Ibraheem

**Department of Mathematics, National University, of Computer and Emerging Sciences, Lahore, Pakistan.**

A. A. Bhatti

A. A. Bhatti

\(^{1}\)Corresponding Author: javaidmath@gmail.com

Copyright © 2018 M. Javaid, M. Ibraheem, A. A. Bhatti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Published:**December, 2018.

### Abstract

Let \(G\) be a simple connected graph with \(V (G)\) and \(E(G)\) as the vertex set and edge set respectively. A topological index is a numeric quantity by which we can characterize the whole structure of a molecular graph or a network to predict the physical or chemical activities of the involved chemical compounds in the molecular graph or network. The connective eccentricity index of the graph \(G\) is defined as \(ξ^{ce}(G) = \sum_{v∈G}\frac{d(v)}{e(v)}\), where \(d(v)\) and \(e(v)\) denote the degree and eccentricity of the vertex \(v ∈ G\) respectively. In this paper, we compute the connective eccentricity index of the various families of the path-thorn graphs and present the obtained results with the help of suitable mathematical expressions consisting on various summations. More precisely, the computed results are general extensions of the some known results.

#### Keywords:

Distance-based index; Eccentricity; Path-thorn graph.