Arc-transitive regular cyclic covers of the complete bipartite graph $$\mathsf{K}_{p,p}$$ K p , p

Two-distance transitive normal Cayley graphs

“…Applying Theorem 1.2, we can obtain the following corollary. The graph Cos(G, a , b ) was first constructed in [19] as a regular cover of K p,p , where it is said that Cos(G, a , b ) is 2-arc-transitive in [19, Theorem 1.1], but not 3-arctransitive generally for all odd primes p in a remark after [19,Example 4.1]. However, this is not true and Corollary 1.3 implies that Cos(G, a , b ) is always 3-arc-transitive for each odd prime p. In fact, Cos(G, a , b ) is 3-arc-regular, that is, Aut(Cos(G, a , b )) is regular on the set of 3-arcs of Cos(G, a , b ).…”

Arc-transitive cyclic and dihedral covers of pentavalent symmetric graphs of order twice a prime

“…For arc-transitive covers of infinite families of graphs, Du et al studied 2-arc-transitive elementary abelian and cyclic covers of complete graphs K n in [10,12] and cyclic covers of K n,n − nK 2 in [31]. Recently, Pan et al [28] determined arc-transitive cyclic covers of the complete bipartite graph K p,p of order 2p for a prime p. Compared with symmetric covers of graphs of small orders and valencies, there are only a few contributions on symmetric covers of infinite families of graphs.…”