Extremal Even Polygonal Chains on Wiener Numbers

AbstractDenote by An the set of h-polygonal chains (where h is even) with n congruent regular h-polygons (h≥6). For any An∈An, let W(An) be the Wiener number of An. In this paper, we show that W(Zn2)≤W(An)≤W(Zn1), with the equalities on the left holding only if An=Zn2, and the equalities on the right holding only if An=Zn1, where Zn1 and Zn2 are extremal chains of type one and type two (their definitions are given in the main text), respectively. Thus we extend the known results of extremal benzenoid chains on Wiener number to a more general case.