Generalised voltage graphs

Potočnik, Primož; Toledo, Micael

doi:10.1016/j.ejc.2021.103313

Cited by 4 publications

(2 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In particular, graph automorphisms that 'commute' with an automorphism of the voltage group have a lift. The following lemma is (broadly speaking) a consequence of the results in [6] and is a particular case of [8,Corollary 22] (where we set ω(x) to be trivial everywhere).…”

Section: Regularitymentioning

confidence: 99%

Faithful and thin non-polytopal maniplexes

Leemans,

Toledo

2024

Ars Math. Contemp.

View full text Add to dashboard Cite

Maniplexes are coloured graphs that generalise maps on surfaces and abstract polytopes. Each maniplex uniquely defines a partially ordered set that encodes information about its structure. When this poset is an abstract polytope, we say that the associated maniplex is polytopal. Maniplexes that have two properties, called faithfulness and thinness, are completely determined by their associated poset, which is often an abstract polytope. We show that all faithful thin maniplexes of rank three are polytopal. So far only one example, of rank four, of a thin maniplex that is not polytopal was known. We construct the first infinite family of maniplexes that are faithful and thin but are non-polytopal for all ranks greater than three.

show abstract

Section: Regularitymentioning

confidence: 99%

Faithful and thin non-polytopal maniplexes

Leemans,

Toledo

2024

Ars Math. Contemp.

View full text Add to dashboard Cite

show abstract

“…We start with a section on preliminaries, including notation, Euclidean space, graphs and realizations of graphs. We then adapt the construction of Potoc ˇnik & Toledo (2021) to the derivation of graphs realized in Euclidean space. But as that construction produces very large graphs of many components, and all we want is one component, we adapt the algorithm of McColm (2015) to obtain (realizations of) the desired crystal nets.…”

Section: Introductionmentioning

confidence: 99%

Realizations of crystal nets. I. (Generalized) derived graphs

McColm

2024

Acta Cryst Sect A

View full text Add to dashboard Cite

A crystal net can be derived from a `generalized' voltage graph representing a graph analog of a fundamental domain of that crystal net along with a sufficient collection of its symmetries. The voltage assignments include not only isometries to the (oriented) edges, but also `weight' groups assigned to vertices for generating the vertex figures around those vertices. By varying the voltage assignments, one obtains geometrically distinct – and occasionally topologically distinct – Euclidean graphs. The focus here is on deriving simple graphs, i.e. graphs with no loops or lunes, especially uninodal edge transitive graphs.

show abstract

Cubic Vertex-Transitive Graphs Admitting Automorphisms of Large Order

Potočnik,

Toledo

2023

Bull. Malays. Math. Sci. Soc.

View full text Add to dashboard Cite

A connected graph of order n admitting a semiregular automorphism of order n/k is called a k-multicirculant. Highly symmetric multicirculants of small valency have been extensively studied, and several classification results exist for cubic vertex- and arc-transitive multicirculants. In this paper, we study the broader class of cubic vertex-transitive graphs of order n admitting an automorphism of order n/3 or larger that may not be semiregular. In particular, we show that any such graph is either a k-multicirculant for some $$k \le 3$$ k ≤ 3 , or it belongs to an infinite family of graphs of girth 6.

show abstract

Generalised voltage graphs

Cited by 4 publications

References 26 publications

Faithful and thin non-polytopal maniplexes

Faithful and thin non-polytopal maniplexes

Realizations of crystal nets. I. (Generalized) derived graphs

Cubic Vertex-Transitive Graphs Admitting Automorphisms of Large Order

Contact Info

Product

Resources

About