A new record of enumeration of regular graphs by parallel processing
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We broke a record, set 8 years ago, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in OEIS, to achieve the number for 4-regular graphs of order 23 as 429,668,180,677,439, while discovering serval optimal regular graphs with minimum diameters. The number of 4-regular graphs and the optimal graphs, extremely time-consuming to calculate, result from a method we adapt from GENREG, a classical regular graph generator, to fit for supercomputers' strengths of using thousands of processor cores.
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