COMPUTATIONAL TECHNIQUES FOR THE AUTOMORPHISM-GROUPS OF GRAPHS

The algorithm developed by Razinger et al. for the automorphism group of a graph is significantly improved by eliminating the CPU-intensive n3 matrix multiplication operations. The CPU times of the two algorithms are compared. The new algorithm based on memory manipulation reduces the required CPU time for some graphs by a factor of approximately 3350. For example, the new algorithm took 1 min, 29 s of CPU time for a graph containing 16 vertices, while the algorithm of Razinger et al. took 82 h, 54 min, 26 s for the same graph on an IBM RS6000/580 system.