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A New Record of Graph Enumeration Enabled by Parallel Processing

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  • Zhipeng Xu

    (School of Data and Computer Science, Sun Yat-sen University, Guangzhou, Guangdong 510006, China
    Guangdong Province Key Laboratory of Computational Science, Guangzhou, Guangdong 510275, China
    Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA)

  • Xiaolong Huang

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA)

  • Fabian Jimenez

    (Department of Technological Operations and High Performance Computing, Empresa Publica Yachay, Urcuquí, Imbabura 100115, Ecuador)

  • Yuefan Deng

    (Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, USA)

Abstract

Using three supercomputers, we broke a record set in 2011, in the enumeration of non-isomorphic regular graphs by expanding the sequence of A006820 in the Online Encyclopedia of Integer Sequences (OEIS), to achieve the number for 4-regular graphs of order 23 as 429,668,180,677,439, while discovering several regular graphs with minimum average shortest path lengths (ASPL) that can be used as interconnection networks for parallel computers. The enumeration of 4-regular graphs and the discovery of minimal-ASPL graphs are extremely time consuming. We accomplish them by adapting GENREG, a classical regular graph generator, to three supercomputers with thousands of processor cores.

Suggested Citation

  • Zhipeng Xu & Xiaolong Huang & Fabian Jimenez & Yuefan Deng, 2019. "A New Record of Graph Enumeration Enabled by Parallel Processing," Mathematics, MDPI, vol. 7(12), pages 1-7, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1214-:d:296034
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