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Classification of Symmetric Tabačjn Graphs

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Abstract

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 \(K_{6,6}-6K_2\) and the icosahedron graph.

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Acknowledgments

The research that led to the results of this paper was conducted during the 2nd Workshop on Abstract Polytopes, held in Cuernavaca, Mexico in August 2012, which was partially supported by the PAPIIT-UNAM under the Project IN106811.

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Authors and Affiliations

  1. Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México, A.P. 273-3 Admon. 3 Cuernavaca, 62251 , Morelos, Mexico

    Aubin Arroyo

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, 04510 , Coyoacán, Mexico

    Isabel Hubard

  3. University of Primorska, FAMNIT, Glagoljaška 8, 6000 , Koper, Slovenia

    Klavdija Kutnar

  4. Instituto de Matemáticas, Universidad Nacional Autónoma de México, 04510 , Coyoacán, Mexico

    Eugenia O’Reilly

  5. Faculty of Education, University of Ljubljana, Kardeljeva ploščad 16, 1000 , Ljubljana, Slovenia

    Primož Šparl

  6. IMFM, Jadranska 19, 1000 , Ljubljana, Slovenia

    Primož Šparl

Authors
  1. Aubin Arroyo
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  2. Isabel Hubard
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  3. Klavdija Kutnar
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  4. Eugenia O’Reilly
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  5. Primož Šparl
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Corresponding author

Correspondence to Klavdija Kutnar.

Additional information

The first author partially supported by CONACyT 167594. The second author partially supported by CONACyT 166951 and by the program “Para las Mujeres en la Ciencia L’Oréal-UNESCO-AMC, 2012”. The third author partially supported by ARRS, P1-0285 and Z1-4006, and by ESF EuroGiga GReGAS. The fifth author partially supported by ARRS, P1-0285, J1-4010 and J1-4021, and by ESF EuroGiga GReGAS.

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Arroyo, A., Hubard, I., Kutnar, K. et al. Classification of Symmetric Tabačjn Graphs. Graphs and Combinatorics 31, 1137–1153 (2015). https://doi.org/10.1007/s00373-014-1447-8

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  • DOI: https://doi.org/10.1007/s00373-014-1447-8

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