Extremal Even Polygonal Chains on Wiener Numbers

Abstract

Denote by ${\mathcal{A}}_n$ the set of h-polygonal chains (where h is even) with n congruent regular h-polygons ($h\ge 6$). For any $A_n\in {\mathcal{A}}_n,$ let $W(A_n)$ be the Wiener number of $A_n.$ In this paper, we show that $W(Z_n^2)\le W(A_n)\le W(Z_n^1),$ with the equalities on the left holding only if $A_n=Z_n^2,$ and the equalities on the right holding only if $A_n=Z_n^1,$ where $Z_n^1$ and $Z_n^2$ 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.

Mathematical subject classification:

• 05C35

Keywords:

• Extremal chain
• polygonal chain
• Wiener number

Additional information

Funding

This project was supported by NSFC grant 11671336 and 11871247.