Energy and Randic index of directed graphs

Abstract

The concept of Randic index has been extended recently for a digraph. We prove that $2R(G)\le \mathcal{E}(G)\le 2\sqrt{\Delta (G)}R(G)$, 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.

11 pages, 2 figures