A Polynomial Time Algorithm for Counting the Number of Independent Sets of Cactus Graphs

Abstract

Counting the number of independent sets of a graph G (denoted as NI(G)) is a classical #P-complete problem for graphs of degree greater or equal than 3. However, there are classes of graphs which according to its topology can be computed in polynomial time. In this paper, we present a polynomial time algorithm for counting the number of independent sets on a special class of graphs called cactus graphs. Our algorithm is based on previous results for counting the number of independent sets on unicyclic graphs.