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arXiv · 2111.10965

Maximum first Zagreb index of orientations of unicyclic graphs with given matching number

Jiaxiang Yang·Hanyuan Deng
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Abstract

Let $D=(V,A)$ be a digraphs without isolated vertices. The first Zagreb index of a digraph $D$ defined as a summation over all arcs, $M_1(D)=\frac{1}{2}\sum\limits_{uv\in A}(d^{+}_{u}+d^{-}_v)$, where $d^{+}_u$(resp. $d^{-}_u$) denotes the out-degree (resp. in-degree) of the vertex $u$. In this paper, we give the maximal values and maximal digraphs of first Zagreb index over the set of all orientations of unicyclic graphs with $n$ vertices and matching number $m$ $(2\leq m\leq \lfloor \frac{n}{2}\rfloor)$.

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Jiaxiang Yang, Hanyuan Deng. 2021-11-22. Maximum first Zagreb index of orientations of unicyclic graphs with given matching number. https://arxiv.org/abs/2111.10965

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