Mathematical Properties of Inverse Sum Index Eccentric Coindices of Graphs

Abstract

Essential and widely studied topological indices, including the well-known Zagreb indices (M<inf>1</inf> and M<inf>2</inf>), and the newly proposed Inverse Sum Indeg Eccentricity Index (ξ<inf>ISI</inf>), To ensure the contributions of all edges within a graph are effectively considered. By emphasizing on the total eccentricity of non-adjacent vertices, Hua et al. introduced the eccentric connectivity coindex (ξc). Inspired by their contributions, we introduce the inverse sum indeg eccentric coindex (ξ<inf>ISI</inf>), which is defined as the ratio of the product of the eccentricities to the sum of the eccentricities for all isolated pair of vertex in a connected graph. This study primarily aims to establish various bounds for ξ<inf>ISI</inf> in finite simple graphs and derives the values of the proposed indices for two specific graph constructions. Additionally, we present a comprehensive set of relationships for ξ<inf>ISI</inf> using several graph products. © 2024 Abdus Salam School of mathematical Sciences. All rights reserved.