Hyper-Wiener Index of \(k\)-Membered Ring Spiro Systems

Xianyong Li1, Xiaofan Yang1, Jian Zhu2, Rongwei Hu3
1College of Computer Science, Chongqing University, Chongqing 400044, P.R.China
2Foundation Department, Xinjiang Polytechnical College, Urumdi 830000, Xinjiang, P.R.China
3College of Mathematic and Systems Science, Xinjiang University, Urumadi 830046, Xinjiang, P.R.China

Abstract

In this paper, the congruence relations and the lower and upper bounds of hyper-Wiener index for \(k\)-membered ring spiro systems given length \(n\) are determined respectively. As these results’ applications,the congruence relations and the extremal five- and six-membered ring spiro systems with maximal and minimal hyper-Wiener index are given respectively.