9-13 June 2013
Koper, Slovenia
UTC timezone
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Cubic symmetric graphs having an abelian automorphism group with two orbits

Presented by Istvan KOVACS
Type: Oral presentation
Track: Symmetries in Graphs, Maps and Other Discrete Structures

Content

Finite connected cubic symmetric graphs of girth $6$ have been classified by K. Kutnar and D. Maru\v{s}i\v{c} ({\it J. Combin. Theory Ser. B} {\bf 99} (2009), 162--184), in particular, each of these graphs has an abelian automorphism group with two orbits on the vertex set. In this paper all cubic symmetric graphs with the latter property are determined. In particular, with the exception of the graphs $K_4, K_{3,3}, Q_3, GP(5,2), GP(10,2), F40$ and $GP(24,5),$ all the obtained graphs are of girth $6$.

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Location: Koper, Slovenia

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