Graph Isomorphism Algorithm by Perfect Matching

Abstract

No polynomial time algorithm is known for the graph isomorphism problern. In this paper, we determine graph isomorphism with the help of perfect matehing algorithm, to Iimit 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 Iabels 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 ) .

Neighborhood hypergraphs of bipartite graphs

“…Our results have obvious algorithmic consequences, since polynomial-time algorithms for graph isomorphism were constructed for many classes of graphs, including trees (Aho, Hopcroft, and Ullman), graphs with bounded vertex degrees (Luks [36], Furst et al [23], and Galil et al [24]), planar graphs (Hopcroft and Tarjan [27,28], Gazit [25], and Ja'Ja' and Kosaraju [29]), interval graphs (Lueker and Booth [35] and Klein [30]), graphs with bounded eigenvalue multiplicities (Babai [4] and Fürer [22]), partial k-trees (Bodlaender [9,10]), graphs with bounded average genus (Chen [15]), convex bipartite graphs (Chen [16]), circulant graphs (Codenotti et al [17]), graphs of bounded distance width (Yamazakiet al [45]), and others, see Hoffmann [26], Köbler et al [31], Babai [5], Campbell and Radford [13], Chen [16], Fukuda and Nakamori [21], Ponomarenko [40,41], Rasin [42], etc.…”