On the Tree with Maximum General Randic Index

Abstract

The general Randic index \(R_{-\alpha}(G)\) of a graph \(G\), defined by a real number \(\alpha\), is the sum of \((d(u)d(v))^{-\alpha}\) over all edges \(uv\) of \(G\), where \(d(u)\) denotes the degree of a vertex \(u\) in \(G\). In this paper, we have discussed some properties of the Max Tree which has the maximum general Randic index \(R_{-\alpha}(G)\), where \(\alpha \in (\alpha_0,2)\). Based on these properties, we are able to obtain the structure of the Max Tree among all trees of order \(k \geq 3\). Thus, the maximal value of \(R_{-\alpha}(G)\) follows easily.