On sufficient condition for t-toughness of a graph in terms of eccentricity-based indices
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Date
2024
Authors
Journal Title
National Academy Science Letters
Journal ISSN
Volume Title
Publisher
Springer
Abstract
Let ?(G) be the number of components of graph G. For t?0 we call G t-tough if t�?(G-X)?|X|, for every X?V(G) with ?(G-X)?2. 1-tough graphs are also called Hamiltonian graphs. The eccentric connectivity index of a connected graph G denoted by ?c(G), is defined as ?c(G)=?v?V(G)?(v)d(v). The eccentric distance sum of a connected graph G is denoted by ?d(G), is defined as ?d(G)=?v?V(G)?(v)D(v). The connective eccentricity index of a connected graph G denoted as ?ce(G), is defined as ?ce(G)=?v?V(G)d(v)?(v), where ?(v) is the eccentricity of the vertex v, D(v) is the sum of the distance from to all other vertices, and d(v) is the degree of vertex v. Finding sufficient conditions for a graph to possess certain properties is a meaningful and important problem. In this article, we give sufficient conditions for t-toughness graphs in terms of the eccentric connectivity index, eccentric distance sum, and connective eccentricity index. � The Author(s), under exclusive licence to The National Academy of Sciences, India 2024.
Description
Keywords
05C09, 05C38, 05C45, Connective eccentricity index, Eccentric distance sum, Graph properties4, Toughness