Infinitely many one-regular Cayley graphs on dihedral groups of any prescribed valency

DOI10.1016/j.jctb.2007.09.005zbMath1142.05043OpenAlexW2087657985MaRDI QIDQ2483481

Young Soo Kwon, Ju-Mok Oh, Jin Ho Kwok

Publication date: 28 April 2008

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jctb.2007.09.005

zbMATH Keywords

Cayley graphsdihedral groupsone-regular graphs

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (15)

A classification of regular \(t\)-balanced Cayley maps on dihedral groups ⋮ Pentavalent symmetric graphs of order twice a prime power ⋮ Arc-transitive dihedrants of odd prime-power order ⋮ ON ARC-REGULAR FROBENIUS METACIRCULANTS ⋮ Pentavalent symmetric graphs of order \(2p^3\) ⋮ On \(G\)-arc-regular dihedrants and regular dihedral maps ⋮ There exist no arc-regular prime-valent graphs of order four times an odd square-free integer ⋮ One-regular graphs of square-free order of prime valency ⋮ Pentavalent symmetric graphs of order \(2pqr\) ⋮ On dihedrants admitting arc-regular group actions ⋮ A classification of regular \(t\)-balanced Cayley maps on dicyclic groups ⋮ Arc-transitive cyclic and dihedral covers of pentavalent symmetric graphs of order twice a prime ⋮ Finite edge-transitive bi-circulants ⋮ Pentavalent One-regular Graphs of Square-free Order ⋮ Symmetric graphs of valency five and their basic normal quotients

Cites Work

• Unnamed Item
• Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree
• On weakly symmetric graphs of order twice a prime
• Regular groups of automorphisms of cubic graphs
• Maps and half-transitive graphs of valency 4
• Automorphism groups of Cayley maps
• Automorphism groups and isomorphisms of Cayley digraphs
• Infinitely many finite one-regular graphs of any even valency.
• Construction of one-regular graphs of valency 4 and 6.
• Classifying arc-transitive circulants
• Permutation groups with a cyclic regular subgroup and arc transitive circulants.
• Constructing an infinite family of cubic 1-regular graphs
• On 1-arc-regular graphs
• Constructing infinite one-regular graphs
• The trivalent symmetric graphs of girth at most six
• A CLASSIFICATION OF PRIME-VALENT REGULAR CAYLEY MAPS ON ABELIAN, DIHEDRAL AND DICYCLIC GROUPS
• Characterisation of Graphs which Underlie Regular Maps on Closed Surfaces
• [https://portal.mardi4nfdi.de/wiki/Publication:4344215 A �-transitive graph of valency 4 with a nonsolvable group of automorphisms]
• On the Classification of Symmetric Graphs with a Prime Number of Vertices
• A One-Regular Graph of Degree Three
• A family of one-regular graphs of valency 4

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