# Classifying cubic symmetric graphs of order 18p2

## 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

*Armenian Journal of Mathematics*,

*12*(1), 1–11. Retrieved from http://armjmath.sci.am/index.php/ajm/article/view/305

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## Section

Articles