Classification of some reflexible edge-transitive embeddings of complete bipartite graphs - Kwak, Jin Ho (Ars mathematica contemporanea, 2019)
In this paper, we classify some reflexible edge-transitive orientable embeddings of complete bipartite graphs. As a by-product, we classify groups ?$Γ$? such that (i) ?$Γ = XY$? for some cyclic groups ?$X = \langle x \rangle$? and ?$Y = \langle y \rangle$? with ?$X \cap Y = \{1_{Γ}\}$? and (ii) there exists an automorphism of ?$Γ$? which sends ?$x$? and ?$y$? to ?$x^{-1}$? and ?$y^{-1}$?, respectively.
Keywords: complete bipartite graphs; polni dvodelni grafi; refleksivna povezavno-tranzitivna vložitev; reflexible edge-transitive embedding