Locally s-arc-transitive graphs arising from product action

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.

Keywords


Locally s-arc-transitive graph, quasiprimitive group, product action

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MANUSCRIPT


DOI: https://doi.org/10.26493/1855-3974.2857.07b

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications