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

Locally s-arc-transitive graphs arising from product action