Graph isomorphism algorithm by perfect matching

No polynomial time algorithm is known for the graph isomorphism problem. In this paper, we determine graph isomorphism with the help of perfect matching algorithm, to limit the range of search of 1 to 1 correspondences between the two graphs: We reconfigure the graphs into layered graphs, labeling vertices by partitioning the set of vertices by degrees. We prepare a correspondence table by means of whether labels on 2 layered graphs match or not. Using that table, we seek a 1 to 1 correspondence between the two graphs. By limiting the search for 1 to 1 correspondences between the two graphs to information in the table, we are able to determine graph isomorphism more efficiently than by other known algorithms. The algorithm was timed with on experimental data and we obtained a complextity of O(n(4)).