A Geometric Approach to Graph Isomorphism.

We present an integer linear program (IP), for the Graph Isomorphism (GI) problem, which has non-empty feasible solution if and only if the input pair of graphs are isomorphic. We study the polytope of the convex hull of the solution points of IP, denoted by B-[2]. Exponentially many facets of this polytope are known. We show that in case of non-isomorphic pairs of graphs if a feasible solution exists for the linear program relaxation (LP) of the IP, then it violates a unique facet of B-[2]. We present an algorithm for GI based on the solution of LP and prove that it detects non-isomorphism in polynomial time if the solution of the LP violates any of the known facets.