Linking rings structures and semisymmetric graphs: Combinatorial constructions

Primož Potočnik, Stephen E. Wilson

Abstract


This paper considers combinatorial methods of constructing LR structures: two isolated constructions, RC and SoP, two closely related constructions, CS(Γ, B, 0) and CS(Γ, B, 1) using cycle decompositions of tetravalent graphs, a generalization of those, CS(Γ, B, k) for k > 2, and finally a construction LDCS relating to cycle decompositions of graphs of higher even valence. This last construction is used to classify all LR structures of types {3, *} or {4, *}.

Keywords


Graph, automorphism group, symmetry, locally arc-transitive graph, semisymmetric graph, cycle structure, linking ring structure

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DOI: https://doi.org/10.26493/1855-3974.1007.3ec

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications