Locally Transitive Graphs Admitting a Group with Cyclic Sylow Subgroups (Communications in Mathematical Research, 2021)
All graphs are finite simple undirected and of no isolated vertices in thispaper. Using the theory of coset graphs and permutation groups, it is completed thata classification of locally transitive graphs admitting a non-Abelian group with cyclicSylow subgroups. They are either the union of the family of arc-transitive graphs, orthe union of the family of bipartite edge-transitive graphs.
Keywords: graph; locally-transitive-graph; Sylow subgroup; cyclic group.