Energy and Randic index of directed graphs

06/30/2021

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by   Gerardo Arizmendi, et al.

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The concept of Randic index has been extended recently for a digraph. We prove that 2R(G)≤ℰ(G)≤ 2√(Δ(G)) R(G), where G is a digraph, and R(G) denotes the Randic index, ℰ(G) denotes the Nikiforov energy and Δ(G) denotes the maximum degree of G. In both inequalities we describe the graphs for which the equality holds.