Linking rings structures and semisymmetric graphs: Combinatorial constructions

Primož Potočnik, Stephen E. Wilson

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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, ∗).

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalArs Mathematica Contemporanea
Issue number1
StatePublished - 2018


  • Automorphism group
  • Cycle structure
  • Graph
  • Linking ring structure
  • Locally arc-transitive graph
  • Semisymmetric graph
  • Symmetry

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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