On the Graphs of Minimum Degree At Least 3 Having Minimum Sum-Connectivity Index

Abstract

For a graph $G$ , its sum-connectivity index is denoted by $\chi \left(G\right)$ and is defined as the sum of the numbers ${\left(d\left(u\right)+d\left(v\right)\right)}^{-1/2}$ over all edges $uv$ of $G$ , where $d\left(w\right)$ denotes the degree of a vertex $w\in V\left(G\right)$ . In this study, we find a sharp lower bound on the sum-connectivity index of graphs having minimum degree of at least 3 under certain constraints and characterize the corresponding extremal graphs.