TY - JOUR
T1 - Linking rings structures and semisymmetric graphs
T2 - Combinatorial constructions
AU - Potočnik, Primož
AU - Wilson, Stephen E.
N1 - Funding Information:
∗Supported in part by Slovenian Research Agency, projects P1-0294. E-mail addresses: primoz.potocnik@fmf.uni-lj.si (Primozˇ Potocˇnik), stephen.wilson@nau.edu (Stephen E.
Publisher Copyright:
© 2018 Society of Mathematicians, Physicists and Astronomers of Slovenia. All Right Reserved.
PY - 2018
Y1 - 2018
N2 - 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, ∗).
AB - 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, ∗).
KW - Automorphism group
KW - Cycle structure
KW - Graph
KW - Linking ring structure
KW - Locally arc-transitive graph
KW - Semisymmetric graph
KW - Symmetry
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U2 - 10.26493/1855-3974.1007.3ec
DO - 10.26493/1855-3974.1007.3ec
M3 - Article
AN - SCOPUS:85047311572
VL - 15
SP - 1
EP - 17
JO - Ars Mathematica Contemporanea
JF - Ars Mathematica Contemporanea
SN - 1855-3966
IS - 1
ER -