The Tight Upper Bound for the Number of Matchings of Tricyclic Graphs

Abstract

In this paper, we determine the tight upper bound for the number of matchings of connected $n$-vertex tricyclic graphs. We show that this bound is $13f_{n-4}+16f_{n-5},$ where $f_{n}$ be the  $n$th Fibonacci number. We also  characterize the $n$-vertex simple connected tricyclic graph for which the bound is best  possible.