Classifying cubic symmetric graphs of order 18p2

Authors

  • Mehdi Alaeiyan Iran University of Science and Technology
  • Mohammad Kazem Hosseinipoor Iran University of Science and Technology
  • Masoumeh Akbarizadeh Iran University of Science and Technology

Keywords:

Symmetric graphs, $s$-regular graphs regular coverings

Abstract

A $s$-arc in a graph is an ordered $(s+1)$-tuple $(v_{0}, v_{1}, \cdots, v_{s-1}, v_{s})$ of vertices such that $v_{i-1}$ is adjacent to $v_{i}$ for $1\leq i \leq s$ and $v_{i-1}\neq v_{i+1}$ for $1\leq i < s$. A graph $X$ is called $s$-regular if its automorphism group acts regularly on the set of its $s$-arcs. In this paper, we classify all connected cubic $s$-regular graphs of order $18p^2$ for each $s\geq1$ and each prime $p$.

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Published

2020-03-28

How to Cite

Alaeiyan, M., Hosseinipoor, M. K., & Akbarizadeh, M. (2020). Classifying cubic symmetric graphs of order 18p2. Armenian Journal of Mathematics, 12(1), 1-11. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/305