On sufficient condition for t-toughness of a graph in terms of eccentricity-based indices

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dc.contributor.authorKori R.
dc.contributor.authorPrasad A.
dc.contributor.authorUpadhyay A.K.
dc.date.accessioned2025-01-13T07:07:59Z
dc.date.available2025-01-13T07:07:59Z
dc.date.issued2024
dc.description.abstractLet ?(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.
dc.identifier.doi10.1007/s40009-024-01437-w
dc.identifier.issn0250541X
dc.identifier.urihttps://dl.bhu.ac.in/ir/handle/123456789/2992
dc.language.isoen
dc.publisherSpringer
dc.subject05C09
dc.subject05C38
dc.subject05C45
dc.subjectConnective eccentricity index
dc.subjectEccentric distance sum
dc.subjectGraph properties4
dc.subjectToughness
dc.titleOn sufficient condition for t-toughness of a graph in terms of eccentricity-based indices
dc.typeArticle
journal.titleNational Academy Science Letters

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