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Research Article

Energy and Randić index of directed graphs

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Pages 2696-2707 | Received 14 Jan 2022, Accepted 18 Jul 2022, Published online: 06 Sep 2022
 

Abstract

The concept of Randić index has been extended recently for a digraph. We prove that 2R(G)E(G)2Δ(G)R(G), where G is a digraph, and R(G) denotes the Randić index, E(G) denotes the Nikiforov energy and Δ(G) 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.

Additional information

Funding

O.A. received support from Conacyt (Consejo Nacional de Ciencia y Tecnología) [grant number CB-2017-2018-A1-S-9764] and from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no 734922.

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