Abstract
The concept of Randić index has been extended recently for a digraph. We prove that , where G is a digraph, and denotes the Randić index, denotes the Nikiforov energy and denotes the maximum degree of G. Moreover, in both inequalities, we describe the graphs for which the equality holds. We also develop the concept of inner and outer energies of a vertex for directed graphs extending important inequalities known for the energy of a vertex for graphs.
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Acknowledgments
The author thanks Roland Speicher and Moritz Weber for the nice environment at University of Saarlands, while visiting for a sabbatical period.
Disclosure statement
No potential conflict of interest was reported by the authors.