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

DOI10.1016/J.AMC.2022.127131arXiv2111.10965WikidataQ114210887 ScholiaQ114210887MaRDI QIDQ6383585

Jiaxiang Yang, Hanyuan Deng

Publication date: 21 November 2021

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, $M_1(D)=frac12sumlimit{s}_{uvinA}(d_u^{+}+d_v^{-})$, 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 $m$ $(2leqmleqlfloorfracn2floor)$.

Mathematics Subject Classification ID

Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Vertex degrees (05C07) Graphical indices (Wiener index, Zagreb index, Randi? index, etc.) (05C09)

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