Automorphisms of Tabacjn graphs

Abstract

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 Tahacjn 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 Tabacjn graphs are vertex-transitive.

On Certain Edge-Transitive Bicirculants of Twice Odd Order

“…The question which of these graphs are edge-transitive has been answered in [9,13,2]. Moreover, the automorphism groups of all (not only the edge-transitive) graphs in the families F(d), d = 3, 4, 5, are also known (see [9,13,8,15]).…”