Bounds for the modified eccentric connectivity index

TL;DR

This paper establishes bounds for the modified eccentric connectivity index of graphs, relating it to various graph parameters, thereby extending the understanding of this generalized graph invariant.

Contribution

It derives new upper and lower bounds for the modified eccentric connectivity index using multiple graph parameters, generalizing previous results.

Findings

Derived bounds in terms of graph parameters like vertices, edges, and degrees

Connected the modified eccentric connectivity index with Zagreb and Wiener indices

Provided theoretical limits for the index based on graph structure

Abstract

The modified eccentric connectivity index of a graph is defined as the sum of the products of eccentricity with the total degree of neighboring vertices, over all vertices of the graph. This is a generalization of eccentric connectivity index. In this paper, we derive some upper and lower bounds for the modified eccentric connectivity index in terms of some graph parameters such as number of vertices, number of edges, radius, minimum degree, maximum degree, total eccentricity, the first and second Zagreb indices, Weiner index etc.