Fourth-Order Randić Index of Phenylenes

Abstract

The higher order connectivity index is a graph invariant defined as ${}^h\chi (G)=\sum _{u_1{u}_2\dots u_{h+1}}\frac{1}{\sqrt{d_{u_1}{d}_{u_2}\dots d_{u_{h+1}}}}$, where the summation is taken over all possible paths of length $h$ and $d_{u_i}$ denotes the degree of the vertex $u_i$ of graph $G$. In this paper, an exact expression for the fourth order connectivity index of Phenylenes is given.