Sharp lower bounds on the sum-connectivity index of quasi-tree graphs.

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 G , respectively. A graph G is called quasi-tree, if there exists u ∈ V (G) such that G − u is a tree. In the paper, we give a sharp lower bound on the sum-connectivity index of quasi-tree graphs. [ABSTRACT FROM AUTHOR]