First and Second Maximum of Randić Index Among all $k-$Cyclic Graphs of a Given Order

Abstract

Suppose $G$ is a simple graph with edge set $E(G)$. The Randić index $R(G)$ is defined as $R(G)={\sum }_{uv\in E(G)}\frac{1}{\sqrt{de{g}_G(u)de{g}_G(v)}}$, where $de{g}_G(u)$ denotes the vertex degree of $u$ in $G$. In this paper, the first and second maximum of Randić index among all $n-$vertex $k-$cyclic graphs were computed.

arXiv comment8 pages