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Open AccessArticle

A New Record of Graph Enumeration Enabled by Parallel Processing

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
Department of Technological Operations and High Performance Computing, Empresa Publica Yachay, Urcuquí, Imbabura 100115, Ecuador
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1214;
Received: 13 November 2019 / Revised: 5 December 2019 / Accepted: 5 December 2019 / Published: 10 December 2019
(This article belongs to the Special Issue Supercomputing and Mathematics)
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. View Full-Text
Keywords: regular graph; parallel computing; dynamical scheduling regular graph; parallel computing; dynamical scheduling
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MDPI and ACS Style

Xu, Z.; Huang, X.; Jimenez, F.; Deng, Y. A New Record of Graph Enumeration Enabled by Parallel Processing. Mathematics 2019, 7, 1214.

AMA Style

Xu Z, Huang X, Jimenez F, Deng Y. A New Record of Graph Enumeration Enabled by Parallel Processing. Mathematics. 2019; 7(12):1214.

Chicago/Turabian Style

Xu, Zhipeng; Huang, Xiaolong; Jimenez, Fabian; Deng, Yuefan. 2019. "A New Record of Graph Enumeration Enabled by Parallel Processing" Mathematics 7, no. 12: 1214.

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