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Arroyo, Aubin; Hubard, Isabel; Kutnar, Klavdija; O’Reilly, Eugenia; Šparl, Primož
Graphs and combinatorics, 09/2015, Letnik: 31, Številka: 5Journal Article
A bicirculant is a graph admitting an automorphism whose cyclic decomposition consists of two cycles of equal length. In this paper we introduce the Tabačjn graphs , a family of pentavalent bicirculants which are a natural generalization of generalized Petersen graphs obtained from them by adding two additional perfect matchings between the two orbits of a semiregular automorphism. The main result is the classification of symmetric Tabačjn graphs. In particular, it is shown that the only such graphs are the complete graph K 6 , the complete bipartite graph minus a perfect matching K 6 , 6 - 6 K 2 and the icosahedron graph.
