Energy and Randic index of directed graphs

Abstract

The concept of Randic index has been extended recently for a digraph. We prove that $2R(G)\leq \mathcal{E}(G)\leq 2\sqrt{\Delta(G)} R(G)$, where $G$ is a digraph, and $R(G)$ denotes the Randic index, $\mathcal{E}(G)$ denotes the Nikiforov energy and $\Delta(G) $ denotes the maximum degree of $G$. In both inequalities we describe the graphs for which the equality holds.