An Upper Bound on the Number of Independent Sets in a Tree

Abstract

The main result of this paper is an upper bound on the number of independent sets in a tree in terms of the order and diameter of the tree. This new upper bound is a refinement of the bound given by Prodinger and Tichy [Fibonacci Q., \(20 (1982), no. 1, 16-21]\). Finally, we give a sufficient condition for the new upper bound to be better than the upper bound given by Brigham, Chandrasekharan and Dutton [Fibonacci Q., \(31 (1993), no. 2, 98-104]\).