Fourth-Order Randić Index of Phenylenes

Abstract

The higher order connectivity index is a graph invariant defined as \(^{h}{}{\chi}(G) = \sum_{u_1u_2\ldots u_{h+1}} \frac{1}{\sqrt{{d_{u_1}d_{u_2}\ldots d_{u_{h+1}}}}}\), 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.