Enumeration of regular graphs by using the cluster in high efficiency
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In this note, we proposed a method to enumerate regular graphs on the cluster in high efficiency after partitioning. Here, we chose the GENREG, a classical regular graph generation, to adapt with supercomputers and clusters by using MPI, which can implement loading balance and support the parallel scale of thousands of CPU cores after task partitioning. Using this method and modified version of the generation, we have got some optimal regular graphs with the minimum diameter. Moreover, we got the exact counting number of 4-regular graphs for order 23, which expand the sequence of A006820 in OEIS. This study improves the efficiency of enumerating regular graphs with current available HPC resources and makes the work of regular graph counting more convenient on the supercomputer.
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