# Classifying cubic symmetric graphs of order $18p^2$

Alaeiyan, Mehdi and Hosseinpoor, Mohammad Kazem and Akbarizadeh, Masoumeh (2020) Classifying cubic symmetric graphs of order $18p^2$. Armenian Journal of Mathematics, 12 (1). pp. 1-11. ISSN 1829-1163

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## 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 $p$.

Item Type: Article Symmetric graphs, $s$-regular graphs regular coverings 05-xx Combinatorics 857 Professor Anry Nersesyan 30 Mar 2020 13:36 30 Mar 2020 13:36

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