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On the Vertex-degree Based Invariants of Digraphs by Deng, Hanyuan; Yang, Jiaxiang; Tang, Zikai; Yang, Jing; You, Meiling is a scholarly article available to read on EtoBox.

What is On the Vertex-degree Based Invariants of Digraphs about?

Let $D=(V,A)$ be a digraphs without isolated vertices. A vertex-degree based invariant $I(D)$ related to a real function $\varphi$ of $D$ is defined as a summation over all arcs, $I(D) = \frac{1}{2}\sum_{uv\in A}{\varphi(d_u^+,d_v^-)}$, where $d_u^+$ (resp. $d_u^-$) denotes the out-degree (resp. in-degree) of a vertex $u$. In this paper, we give the extremal values and extremal digraphs of $I(D)$ over all digraphs with $n$ non-isolated vertices. Applying these results, we obtain the extremal values of some vertex-degree based topological indices of digraphs, such as the Randi\'{c} index, the Zagreb index, the sum-connectivity index, the $GA$ index, the $ABC$ index and the harmonic index, and the corresponding extremal digraphs.

Author

Deng, Hanyuan; Yang, Jiaxiang; Tang, Zikai; Yang, Jing; You, Meiling

Published

2021

Language

EN