Abstract
Finding the maximum independent set (or stable set) of any graph is an important problem in graph theory that has many applications such as computer vision/pattern recognition, information/coding theory, molecular biology and scheduling. In this paper we propose a quadrating programming formulation for finding the maximum independent set of any graph from the maximal cliques of the graph. It is proved in the computing science literature, there exist near optimum algorithms to list the maximal cliques of sparse graphs. Accordingly, we except our formulation to be of value in finding the maximum independent set and the independence number of sparse graphs from the computational complexity standpoint. Using our formulation, we were able to find the unknown maximum independent set and independence number for some known graphs such as Gardner graph, Balaban 11 cage graph and Hoffman-Singleton line graph.