3 research outputs found
The number of independent sets in bipartite graphs and benzenoids
Given a graph , we study the number of independent sets in , denoted
. This parameter is known as both the Merrifield-Simmons index of a graph
as well as the Fibonacci number of a graph. In this paper, we give general
bounds for when is bipartite and we give its exact value when is
a balanced caterpillar. We improve upon a known upper bound for when
is a tree, and study a conjecture that all but finitely many positive integers
represent for some tree . We also give exact values for when
is a particular type of benzenoid