Armenian Journal of Mathematics, 12(1)
2022; 1–11
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Classifying cubic symmetric graphs of order 18 p2

Mehdi Alaeiyan*, Mohammad Kazem Hosseinipoor, Masoumeh Akbarizadeh

Received: 2024-12-10 · Published: 2022-08-28

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CC BY 4.0 This work is licensed under a Creative Commons Attribution 4.0 International License.
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Original title
Classifying cubic symmetric graphs of order 18 p2
Authors
Mehdi Alaeiyan, Mohammad Kazem Hosseinipoor, Masoumeh Akbarizadeh
Source journal
Armenian Journal of Mathematics, 12(1)
Published
2022-08-28
Licence
Creative Commons Attribution 4.0 International
Original
https://doi.org/10.52737/18291163-2020.12.1-1-11

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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