Maximum zeroth-order general Randi\'{c} index of orientations of trees, unicyclic and bicyclic graphs with given matching number

Abstract

The zeroth-order general Randi\'{c} index $R^{0}_{a}$ of a digraph $D$ is the sum of $(d^{+}_{v})^{a}+(d^{-}_{w})^{a}$ over all arcs $vw$ of $D$, where $a$, $d^{+}_{v}$ and $d^{-}_{w}$ are an arbitrary real number, the out-degree of the vertex $v$ and the in-degree of the vertex $w$, respectively. We determine maximum zeroth-order general Randi\'{c} index of oriented trees, unicyclic and bicyclic graphs in terms of matching number and order in this paper.