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    Author(s)

    Mehdi Alaeiyan, PhD. Mohammad Kazem Hosseinipoor — Academia (Universities, Colleges and other higher learning entities) (Iran University of Science and Technology), PhD. Masoumeh Akbarizadeh — Academia (Universities, Colleges and other higher learning entities) (Iran University of Science and Technology)
    Category: Mathematics
    DOI: 10.52737/18291163-2020.12.1-1-11
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      Classifying cubic symmetric graphs of order 18 p2

      Mehdi Alaeiyan, PhD. Mohammad Kazem Hosseinipoor — Academia (Universities, Colleges and other higher learning entities) (Iran University of Science and Technology), PhD. Masoumeh Akbarizadeh — Academia (Universities, Colleges and other higher learning entities) (Iran University of Science and Technology)
      This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

      Submitted: 2024-12-09; Published: 2022-08-28
      © 2025 by author(s) and The Gufo Inc.
      CC BY-NC 4.0 This work is licensed under Creative Commons Attribution–NonCommercial International License (CC BY-NC 4.0).

      Abstract

      A ss-arc in a graph is an ordered (s+1)(s+1)-tuple (v0,v1,⋯,vs−1,vs)(v0,v1,⋯,vs−1,vs) of vertices such that vi−1vi−1 is adjacent to vivi for 1≤i≤s1≤i≤s and vi−1≠vi+1vi−1≠vi+1 for 1≤i<s1≤i<s. A graph XX is called ss-regular if its automorphism group acts regularly on the set of its ss-arcs. In this paper, we classify all connected cubic ss-regular graphs of order 18p218p2 for each s≥1s≥1 and each prime pp.

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