Geodesic
Locally s-arc-transitive graphs arising from product action
Ars Mathematica Contemporanea, Tome 23 (2023) no. 2, article no. 10, 14 p.

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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.
DOI : 10.26493/1855-3974.2857.07b
Keywords: Locally s-arc-transitive graph, quasiprimitive group, product action 
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Michael Giudici; Eric Swartz. Locally s-arc-transitive graphs arising from product action. Ars Mathematica Contemporanea, Tome 23 (2023) no. 2, article  no. 10, 14 p. doi : 10.26493/1855-3974.2857.07b. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2857.07b/

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