Regular embeddings of \(K_{n,n}\) where \(n\) is a power of 2. II: The non-metacyclic case

DOI10.1016/j.ejc.2010.01.009zbMath1221.05079OpenAlexW2046795297MaRDI QIDQ709265

Martin Škoviera, Gareth A. Jones, Shao-Fei Du, Roman Nedela, Jin Ho Kwok

Publication date: 18 October 2010

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

Full work available at URL: https://doi.org/10.1016/j.ejc.2010.01.009

zbMATH Keywords

regular orientable embeddings of complete bipartite graphs

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graph representations (geometric and intersection representations, etc.) (05C62) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Related Items (28)

Complete circular regular dessins of type \(\{2^e,2^f\}\). I: metacyclic case ⋮ Complete regular dessins of odd prime power order ⋮ Nonorientable regular embeddings of graphs of order \(p^3\) ⋮ On nilpotent orientably-regular maps of nilpotency class \(4\) ⋮ Galois action on families of generalised Fermat curves ⋮ Regular maps of graphs of order \(4p\) ⋮ On even-closed regular embeddings of graphs ⋮ Edge-transitive uniface embeddings of bipartite multi-graphs ⋮ On the orientably-regular embeddings of graphs of order prime-cube ⋮ Classification of regular embeddings of \(n\)-dimensional cubes ⋮ On the orientable regular embeddings of complete multipartite graphs ⋮ Reflexible complete regular dessins and antibalanced skew morphisms of cyclic groups ⋮ A class of orientably-regular embeddings of graphs of order \(p^3\) ⋮ Orientably-regular \(p\)-maps and regular \(p\)-maps ⋮ Regular maps with nilpotent automorphism groups ⋮ A classification of orientably-regular embeddings of complete multipartite graphs ⋮ Circular regular dessins ⋮ Complete bipartite multi-graphs with a unique regular dessin ⋮ A classification of orientably edge-transitive circular embeddings of \(\mathbf{K}_{p^e, p^f}\) ⋮ Classification of nonorientable regular embeddings of complete bipartite graphs ⋮ Nonorientable regular embeddings of graphs of order \(pq\) ⋮ Orientably-regular embeddings of a class of multipartite graphs ⋮ Regular maps with nilpotent automorphism group ⋮ Classification of some reflexible edge-transitive embeddings of complete bipartite graphs ⋮ Complete regular dessins and skew-morphisms of cyclic groups ⋮ The complete bipartite graphs which have exactly two orientably edge-transitive embeddings ⋮ Complete circular regular dessins of coprime orders ⋮ Bipartite graph embeddings, Riemann surfaces and Galois groups

Cites Work

• Operators over regular maps
• Regular embeddings of \(K_{n,n}\) where \(n\) is a power of 2. I: Metacyclic case
• Regular embeddings of \(K_{n,n}\) where \(n\) is an odd prime power
• Complete bipartite graphs with a unique regular embedding
• Classification of reflexible regular embeddings and self-Petrie dual regular embeddings of complete bipartite graphs
• 2-Groups that factorise as products of cyclic groups, and regular embeddings of complete bipartite graphs
• Endliche Gruppen I
• Unnamed Item

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