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Classification of the pentavalent symmetric graphs of order 18p

Author

Listed:
  • Mehdi Alaeiyan

    (Iran University of Science and Technology)

  • Masoumeh Akbarizadeh

    (Iran University of Science and Technology)

Abstract

A graph is symmetric if its automorphism group is transitive on the arc set of the graph. In this paper, we give a complete classification of connected pentavalent symmetric graphs of order 18p, for each prime p. It is shown that, such graphs there exist if and only if p = 2, 7 or 19, and up to isomorphism, there are only four such graphs.

Suggested Citation

  • Mehdi Alaeiyan & Masoumeh Akbarizadeh, 2019. "Classification of the pentavalent symmetric graphs of order 18p," Indian Journal of Pure and Applied Mathematics, Springer, vol. 50(2), pages 485-497, June.
    • Handle: RePEc:spr:indpam:v:50:y:2019:i:2:d:10.1007_s13226-019-0340-9
    DOI: 10.1007/s13226-019-0340-9
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    Cited by:

    1. Ben Gong Lou & Shi Xin Wang, 2023. "Pentavalent symmetric graphs of order $$8p^2$$ 8 p 2," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(1), pages 253-258, March.
    2. Masoumeh Akbarizadeh & Mehdi Alaeiyan & Raffaele Scapellato, 2020. "Pentavalent 1-Transitive Digraphs with Non-Solvable Automorphism Groups," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1919-1930, December.

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