Locally 3-Arc-Transitive Regular Covers of Complete Bipartite Graphs

Eric Swartz

Abstract


In this paper, locally $3$-arc-transitive regular covers of complete bipartite graphs are studied, and results are obtained that apply to arbitrary covering transformation groups. In particular, methods are obtained for classifying the locally $3$-arc-transitive graphs with a prescribed covering transformation group, and these results are applied to classify the locally $3$-arc-transitive regular covers of complete bipartite graphs with covering transformation group isomorphic to a cyclic group or an elementary abelian group of order $p^2$.

Keywords


Locally $s$-arc-transitive graphs; Graph automorphisms; Regular covers; Group actions

Full Text:

PDF