Energy and Randic index of directed graphs
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...
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| description | 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. |
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| subjects | Graph theory Graphs |
| title | Energy and Randic index of directed graphs |
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