Linking Rings Structures and tetravalent semisymmetric graphs

Primož Potočnik, Stephen E. Wilson

Abstract


In this paper, we introduce LR structures, a new and interesting form of symmetry in graphs. LR structures are motivated by the search for semisymmetric graphs of degree 4. We show that all semisymmetric graphs of girth and degree 4 can be constructed in a simple way from LR structures. We then show several ways in which LR structures can be constructed or found.


Keywords


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

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DOI: https://doi.org/10.26493/1855-3974.311.4a8

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