The higher order connectivity index is a graph invariant defined as h X (G)=Σu1 u2 u h+1 (du1 d u2 duh=1) -1/2, where the summation is taken over all possible paths of length h, and d u i denotes the degree of the vertex uI of the graph G. In this paper, we stick to researching the fourth order connected index of hexagonal chains and give a calculation formula and we characterize the extremal graphs with the extremal fourth-order Randi¢ index.

Luozhong Gong, Meichun Zhao and Jing Chen