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Classification of the pentavalent symmetric graphs of order 18p

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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.

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Authors and Affiliations

  1. Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16844, Iran

    Mehdi Alaeiyan & Masoumeh Akbarizadeh

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  1. Mehdi Alaeiyan
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  2. Masoumeh Akbarizadeh
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Correspondence to Mehdi Alaeiyan or Masoumeh Akbarizadeh.

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Alaeiyan, M., Akbarizadeh, M. Classification of the pentavalent symmetric graphs of order 18p. Indian J Pure Appl Math 50, 485–497 (2019). https://doi.org/10.1007/s13226-019-0340-9

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  • DOI: https://doi.org/10.1007/s13226-019-0340-9

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