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Classifying Seven-Valent Symmetric Graphs of Order 8 pq

Author

Listed:
  • Yingbi Jiang

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031, China)

  • Bo Ling

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031, China)

  • Jinlong Yang

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031, China)

  • Yun Zhao

    (School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031, China)

Abstract

A graph is symmetric if its automorphism group is transitive on the arcs of the graph. Guo et al. determined all of the connected seven-valent symmetric graphs of order 8 p for each prime p . We shall generalize this result by determining all of the connected seven-valent symmetric graphs of order 8 p q with p and q to be distinct primes. As a result, we show that for each such graph of Γ , it is isomorphic to one of seven graphs.

Suggested Citation

  • Yingbi Jiang & Bo Ling & Jinlong Yang & Yun Zhao, 2024. "Classifying Seven-Valent Symmetric Graphs of Order 8 pq," Mathematics, MDPI, vol. 12(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:6:p:787-:d:1352865
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    References listed on IDEAS

    as
    1. Renbing Xiao & Xiaojiao Zhang & Hua Zhang, 2023. "On Edge-Primitive Graphs of Order as a Product of Two Distinct Primes," Mathematics, MDPI, vol. 11(18), pages 1-10, September.
    2. Song-Tao Guo, 2020. "Classifying Heptavalent Symmetric Graphs of Order 40p," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1893-1901, December.
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