Hyper-Wiener Index of $k$-Membered Ring Spiro Systems

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.