Hosoya index of tree structures

Abstract

‎‎‎The Hosoya index‎, ‎also known as the $Z$ index‎, ‎of a graph is the‎ ‎total number of matchings in it‎. ‎In this paper‎, ‎we study the Hosoya index of the tree structures‎. ‎Our aim is to give some results on $Z$ in terms of Fibonacci numbers‎ ‎in such structures‎. ‎Also‎, ‎the asymptotic normality of this index is given‎.