The hexagonal chains with the extremal third-order Randić index

The third-order Randić index of a graph G is defined as R 3 ( G ) = ∑ u 1 u 2 u 3 u 4 1 d ( u 1 ) d ( u 2 ) d ( u 3 ) d ( u 4 ) , where the summation is taken over all possible paths of length three of G . A recursive formula for computing the third-order Randić index of a hexagonal chain is given in this paper, and the hexagonal chains with the extremal third-order Randić index are characterized.