The hexagonal chains with the extremal third-order Randić index

The third-order Randić index of a graph GG is defined as R3(G)=∑u1u2u3u41d(u1)d(u2)d(u3)d(u4), where the summation is taken over all possible paths of length three of GG. 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.