Maximum zeroth-order general Randić index of orientations of trees, unicyclic and bicyclic graphs with given matching number

Abstract

The zeroth-order general Randić index $R_a^0$ 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 Randić index of oriented trees, unicyclic and bicyclic graphs in terms of matching number and order in this paper.

arXiv admin note: text overlap with arXiv:2111.10965