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Automorphisms of Tabačjn graphs

Kutnar Klavdija (University of Primorska, FAMNIT, Koper, Slovenia)
Marušič Dragan (University of Primorska, FAMNIT, Koper, Slovenia)
Miklavič Štefko (University of Primorska, FAMNIT, Koper, Slovenia)
Strašek Rok (University of Primorska, FM, Koper, Slovenia)

A bicirculant is a graph admitting an automorphism whose cyclic decomposition consists of two cycles of equal length. In this paper we consider automorphisms of the so-called Tahačjn graphs, a family of pentavalent bicirculants which are obtained from the generalized Petersen graphs by adding two additional perfect matchings between the two orbits of the above mentioned automorphism. As a corollary, we determine which Tabačjn graphs are vertex-transitive.

Keywords: pentavalent graph, bicirculant, automorphism group, vertex-transitive