Locally s-arc-transitive graphs arising from product action

Michael Giudici; Eric Swartz

Locally s-arc-transitive graphs arising from product action

Combinatorics 2022-03-31 v1

Authors: Michael Giudici , Eric Swartz

Abstract

We study locally $s$ -arc-transitive graphs arising from the quasiprimitive product action (PA). We prove that, for any locally $(G,2)$ -arc-transitive graph with $G$ acting quasiprimitively with type PA on both $G$ -orbits of vertices, the group $G$ does not act primitively on either orbit. Moreover, we construct the first examples of locally $s$ -arc-transitive graphs of PA type that are not standard double covers of $s$ -arc-transitive graphs of PA type, answering the existence question for these graphs.

Cite

@article{arxiv.2203.16522,
  title  = {Locally s-arc-transitive graphs arising from product action},
  author = {Michael Giudici and Eric Swartz},
  journal= {arXiv preprint arXiv:2203.16522},
  year   = {2022}
}

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