A Sharp Lower Bound of Index of the Cacti with Perfect Matchings

Abstract

The Randić index of an organic molecule whose molecular graph is \(G\) is the sum of the weights \((d(u)d(v))^{-\frac{1}{2}}\) of all edges \(uv\) of \(G\), where \(d(u)\) and \(d(v)\) are the degrees of the vertices \(u\) and \(v\) in \(G\). In this paper, we give a sharp lower bound on the Randić index of cacti with perfect matchings.