### Abstract

Original language | English |
---|---|

Pages (from-to) | 167-186 |

Number of pages | 20 |

Journal | Journal of Algebra |

Volume | 421 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

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### Cite this

*Journal of Algebra*,

*421*, 167-186. https://doi.org/10.1016/j.jalgebra.2014.08.025

}

*Journal of Algebra*, vol. 421, pp. 167-186. https://doi.org/10.1016/j.jalgebra.2014.08.025

**On the orders of arc-transitive graphs.** / Conder, M.D.E.; Li, Cai-Heng; Potočnik, P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the orders of arc-transitive graphs

AU - Conder, M.D.E.

AU - Li, Cai-Heng

AU - Potočnik, P.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - © 2014 Elsevier Inc. A graph is called arc-transitive (or symmetric) if its automorphism group has a single orbit on ordered pairs of adjacent vertices, and 2-arc-transitive its automorphism group has a single orbit on ordered paths of length 2. In this paper we consider the orders of such graphs, for given valency. We prove that for any given positive integer k, there exist only finitely many connected 3-valent 2-arc-transitive graphs whose order is kp for some prime p, and that if d≥4, then there exist only finitely many connected d-valent 2-arc-transitive graphs whose order is kp or kp2 for some prime p. We also prove that there are infinitely many (even) values of k for which there are only finitely many connected 3-valent symmetric graphs of order kp where p is prime.

AB - © 2014 Elsevier Inc. A graph is called arc-transitive (or symmetric) if its automorphism group has a single orbit on ordered pairs of adjacent vertices, and 2-arc-transitive its automorphism group has a single orbit on ordered paths of length 2. In this paper we consider the orders of such graphs, for given valency. We prove that for any given positive integer k, there exist only finitely many connected 3-valent 2-arc-transitive graphs whose order is kp for some prime p, and that if d≥4, then there exist only finitely many connected d-valent 2-arc-transitive graphs whose order is kp or kp2 for some prime p. We also prove that there are infinitely many (even) values of k for which there are only finitely many connected 3-valent symmetric graphs of order kp where p is prime.

U2 - 10.1016/j.jalgebra.2014.08.025

DO - 10.1016/j.jalgebra.2014.08.025

M3 - Article

VL - 421

SP - 167

EP - 186

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -