Abstract
The sum-connectivity index of a graph G is defined as the sum of weights 1 / d u + d v over all edges u v of G , where d u and d v are the degrees of the vertices u and v in graph G , respectively. In this paper, we give a sharp lower bound on the sum-connectivity index unicyclic graphs of order n ≥ 7 and diameter D G ≥ 5 .
Highlights
Introduction and PreliminariesA topological index is a numeric number associated with a molecular graph that correlates certain physicochemical properties of chemical compounds. e topological indices are useful in the prediction of physicochemical properties and the bioactivity of the chemical compounds [1,2,3]
Topological indices invariants are used for Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) studies
Let G be any unicyclic graph and U be a diametral path of G
Summary
Department of Mathematics and Computer Science, Basic Science Faculty, University of Bonab, P.O. Box 55513-95133, Bonab, Iran Received 1 August 2021; Revised 17 August 2021; Accepted 23 August 2021; Published 2 September 2021 e sum-connectivity index of a graph G is defined as the sum of weights 1/ du + dv over all edges uv of G, where du and dv are the degrees of the vertices u and v in graph G, respectively. In this paper, we give a sharp lower bound on the sum-connectivity index unicyclic graphs of order n ≥ 7 and diameter D(G) ≥ 5.
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