Extremal Zeroth-Order General Randic Index Of Thorn Graphs

Abstract

Let $G=(V,E)$ be a simple connected graph, where $d_v$ is the degree of vertex $v$. The zeroth-order Randić index of $G$ is defined as $R_n^0(G)=\sum _{v\in V}{d}_v^{\alpha }$, where $\alpha$ is an arbitrary real number. Let $G^{\ast }$ be the thorn graph of $G$ by attaching $d_G(v_i)$ new pendent edges to each vertex $v_i$ ($1\le i\le n$) of $G$. In this paper, we investigate the zeroth-order general Randić index of a class thorn tree and determine the extremal zeroth-order general Randić index of the thorn graphs $G^{\ast }(n,m)$.