Arc-transitive regular cyclic covers of the complete bipartite graph \(\mathsf{K}_{p,p}\)
Characterizing regular covers of edge-transitive or arc-transitive graphs is currently a hot topic in algebraic graph theory. In this paper, we will classify arc-transitive regular cyclic covers of the complete bipartite graph \(\mathsf{K}_{p,p}\) for each odd prime \(p\). The classification consists of four infinite families of graphs. In particular, such covers exist for each odd prime \(p\). The regular elementary abelian covers of \(\mathsf{K}_{p,p}\) are considered in a sequel.
complete bipartite graph regular cover arc-transitive graph cayley graph 20b15 20b30 05c25