Classifying cubic symmetric graphs of order 18p2
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Republic of Armenia National Academy of Sciences
2020-03-01
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| Series: | Armenian Journal of Mathematics |
| Subjects: | |
| Online Access: | http://test.armjmath.sci.am/index.php/ajm/article/view/305 |
| Summary: | 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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| ISSN: | 1829-1163 |