A Practical Graph Isomorphism Algorithm with Vertex Canonical Labeling

The vertex canonical labeling technique is one of the powerful methods in solving the graph isomorphism problem. However, some famous algorithms relied upon this technique are incomplete due to their non-zero probability of rejection. In this paper, we advance a new method of vertex canonical labeling and propose a complete graph isomorphism algorithm with depth-first backtracking. The time complexity of this algorithm is O(n^α) where n^α is the number of backtracking points and (h-1)/2≤α≤(h+1)/2 for h=log in most cases. Finally, the proposed algorithm is compared with other researches on many types of graphs. The performance results validated that our algorithm is efficient for a wide variety of families of graphs.