Pentavalent Symmetric Graphs of Order $12p$

  • Song-Tao Guo
  • Jin-Xin Zhou
  • Yan-Quan Feng


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 $p=11$.

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