A visual tool for determining the maximum independent set of a graph using the polynomial formulation method

Abstract

Maximum independent set is a prototype problem in a graph theory that has many applications in engineering and science. In this paper, we study the problem of determining the largest number of maximum independent sets of a graph G (V, E) of order n using polynomial formulations. This method uses the first and second order neighbourhoods of nodes to determine whether a node is in the maximum independent set. This involves the maximization of an n-variable polynomial, where n is the number of nodes in G. Finally, we present a visual tool developed using the Visual C++ programming language for solving the maximum independent set problem.