On the Zeroth-Order General Randić Index of Cacti

Abstract

The zeroth-order general Randić index of a graph \(G\) is defined as \({}^{0}{}{R}_\alpha = \sum\limits_{v\in V(G)} d(v)^\alpha\)
where \(d(v)\) is the degree of the vertex \(v\) in \(G\) and \(\alpha\) is an arbitrary real number. In the paper, we give sharp lower and upper bounds on the zeroth-order general Randić index of cacti.