Geodesic
Pentavalent symmetric graphs of order 12\(p\)
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In this paper, a complete classification of connected pentavalent symmetric graphs of order $12p$ is given for each prime $p$. As a result, a connected pentavalent symmetric graph of order $12p$ exists if and only if $p=2$, $3$, $5$ or $11$, and up to isomorphism, there are only nine such graphs: one for each $p=2$, $3$ and $5$, and six for $p=11$.
DOI : 10.37236/720
Classification : 05C25, 05C60, 20B25
Mots-clés : symmetric graph, \(s\)-arc-transitive graph, \(s\)-transitive graph 
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     author = {Song-Tao Guo and Jin-Xin Zhou and Yan-Quan Feng},
     title = {Pentavalent symmetric graphs of order 12\(p\)},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/720},
     zbl = {1243.05106},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/720/}
}
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Song-Tao Guo; Jin-Xin Zhou; Yan-Quan Feng. Pentavalent symmetric graphs of order 12\(p\). The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/720

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