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 \(R^0_n(G) = \sum_{v \in V} d_v^\alpha\), where \(\alpha\) is an arbitrary real number. Let \(G^*\) be the thorn graph of \(G\) by attaching \(d_G(v_i)\) new pendent edges to each vertex \(v_i\) (\(1 \leq i \leq n\)) 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 \(G^*(n,m)\).