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.
Original language | English (US) |
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Journal | Mathematics |
Volume | 7 |
Issue number | 12 |
DOIs | |
State | Published - Dec 1 2019 |
Keywords
- Dynamical scheduling
- Parallel computing
- Regular graph
ASJC Scopus subject areas
- Computer Science (miscellaneous)
- General Mathematics
- Engineering (miscellaneous)