Four Constructions of Highly Symmetric Tetravalent Graphs

Art Discrete Appl. Math.

Wilson

2020

“…HC(Λ) is clearly a fourfold cover of L(Λ); it is sometimes but not always a twofold cover of DG(Λ). The Hill Capping is described more fully in [15].…”

Section: Hill Cappingmentioning

confidence: 99%

Recipes for edge-transitive tetravalent graphs

Art Discrete Appl. Math.

Wilson

2020

“…Let Λ be a cubic graph. Then its dart graph Dart(Λ) is the graph whose vertex set consists of all the arcs (called darts in [4]…”

Section: 2mentioning

confidence: 99%

On the radius and the attachment number of tetravalent half-arc-transitive graphs

Šparl

2017

Discrete Mathematics

In this paper, we study the relationship between the radius r and the attachment number a of a tetravalent graph admitting a half-arctransitive group of automorphisms. These two parameters were first introduced in [J. Combin. Theory Ser. B 73 (1998), 41-76], where among other things it was proved that a always divides 2r. Intrigued by the empirical data from the census [Ars Math. Contemp. 8 (2015)] of all such graphs of order up to 1000 we pose the question of whether all examples for which a does not divide r are arc-transitive. We prove that the answer to this question is positive in the case when a is twice an odd number. In addition, we completely characterize the tetravalent graphs admitting a half-arc-transitive group with r = 3 and a = 2, and prove that they arise as non-sectional split 2-fold covers of line graphs of 2-arc-transitive cubic graphs.2010 Mathematics Subject Classification. 05C25, 20B25.

“…Following [6], for a digraph Γ, we let the dart digraph of Γ (denoted DΓ) be the the digraph with vertices and darts being the darts and 2-darts of Γ, respectively. Note that the dart digraph is always reversible with a reversal which maps a dart (u, v) to its inverse dart (v, u).…”

Section: Relationship With a 2 G(λ)mentioning

confidence: 99%

The separated box product of two digraphs

European Journal of Combinatorics

Wilson

2017

Self Cite

A new product construction of graphs and digraphs, based on the standard box product of graphs and called the separated box product, is presented, and several of its properties are discussed. Questions about the symmetries of the product and their relations to symmetries of the factor graphs are considered. An application of this construction to the case of tetravalent edge-transitive graphs is discussed in detail.2000 Mathematics Subject Classification. 20B25.