Linking rings structures and semisymmetric graphs: Cayley constructions |
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| Institution: | 1. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia;2. Northern Arizona University, Department of Mathematics and Statistics, Box 5717, Flagstaff, AZ 86011, USA |
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| Abstract: | An LR structure is a tetravalent vertex-transitive graph together with a special type of a decomposition of its edge-set into cycles. LR structures were introduced in Potočnik and Wilson (2014) as a tool to study tetravalent semisymmetric graphs of girth 4. In this paper, we consider algebraic methods of constructing LR structures, using number theory, Cayley graphs, affine groups, abelian groups and fields. |
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