A classification of regular \(t\)-balanced Cayley maps on dicyclic groups

DOI10.1016/J.EJC.2007.06.023zbMath1165.05013OpenAlexW2005289556MaRDI QIDQ925018

Ju-Mok Oh, Jin Ho Kwok

Publication date: 29 May 2008

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2007.06.023

zbMATH Keywords

automorphism groupCayley graphCayley mapdicyclic groups

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Geometric group theory (20F65) Enumeration in graph theory (05C30) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Cites Work

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• Regular maps from Cayley graphs. I: Balanced Cayley maps
• A classification of regular \(t\)-balanced Cayley maps on dihedral groups
• Regular maps from Cayley graphs. III: \(t\)-balanced Cayley maps
• Regular \(t\)-balanced Cayley maps
• Groups with sign structure and their antiautomorphisms
• Regular maps from Cayley graphs. II: Antibalanced Cayley maps
• Automorphism groups of Cayley maps
• Skew-morphisms of regular Cayley maps
• Infinitely many finite one-regular graphs of any even valency.
• Construction of one-regular graphs of valency 4 and 6.
• Constructing one-regular graphs of valency 4\(k\) with non-cyclic vertex stabilizer
• Infinitely many one-regular Cayley graphs on dihedral groups of any prescribed valency
• One-regular normal Cayley graphs on dihedral groups of valency 4 or 6 with cyclic vertex stabilizer
• Cayley maps
• Regular balanced Cayley maps for cyclic, dihedral and generalized quaternion groups
• On balanced Cayley maps over abelian groups

Related Items (21)

On the direct products of skew-morphisms ⋮ On the skew-morphisms of dihedral groups ⋮ Regular maps from Cayley graphs. III: \(t\)-balanced Cayley maps ⋮ Quotients of polynomial rings and regular \(t\)-balanced Cayley maps on abelian groups ⋮ On \(G\)-arc-regular dihedrants and regular dihedral maps ⋮ Classification of reflexible Cayley maps for dihedral groups ⋮ Regular \(t\)-balanced Cayley maps for Abelian groups ⋮ Regular balanced Cayley maps on nonabelian metacyclic groups of odd order ⋮ Regular Cayley maps of skew-type 3 for abelian groups ⋮ Unnamed Item ⋮ Regular maps from Cayley graphs. I: Balanced Cayley maps ⋮ Regular Cayley maps for cyclic groups ⋮ Regular \(t\)-balanced Cayley maps on semi-dihedral groups ⋮ Regular balanced Cayley maps on \(\operatorname{PSL}(2,p)\) ⋮ Regular Cayley maps on dihedral groups with the smallest kernel ⋮ A classification of regular \(t\)-balanced Cayley maps on \(\mathbb{Z}_2\)-extensions of a cyclic 2-group ⋮ Smooth skew morphisms of the dihedral groups ⋮ Smooth skew morphisms of dicyclic groups ⋮ Regular Cayley maps of skew-type 3 for dihedral groups ⋮ A classification of regular Cayley maps with trivial Cayley-core for dihedral groups ⋮ Classification of skew morphisms of cyclic groups which are square roots of automorphisms

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