A graph is called cubic (respectively tetravalent) if all of its vertices have valency 3
(respectively valency 4). It is called vertex-transitive (respectively arc-transitive) if its …

The main result of this paper is that, if Γ is a connected 4-valent G-arc-transitive graph and v
is a vertex of Γ, then either Γ is part of a well-understood infinite family of graphs, or| G v|≤ 2 …

Recipes for edge-transitive tetravalent graphs* Page 1 ISSN 2590-9770 The Art of Discrete
and Applied Mathematics 3 (2020) #P1.08 https://doi.org/10.26493/2590-9770.1269.732 (Also …

Let p be a prime and let L be either the intransitive permutation group C p× C p of degree 2p
or the transitive permutation group C p wr C 2 of degree 2p. Let Γ be a connected G-vertex …

This paper is to accompany the Census of Edge-Transitive Tetravalent Graphs, available at
jan. ucc. nau. edu/~ swilson/C4FullSite/index. html, which is a collection of all known edge …

We develop a new framework for analysing finite connected, oriented graphs of valency 4,
which admit a vertex-transitive and edge-transitive group of automorphisms preserving the …

We consider tetravalent graphs within a family introduced by Praeger and Xu in 1989. These
graphs have the property of having exceptionally large symmetry groups among all …

In this paper we study G-arc-transitive graphs Δ where the permutation group induced by the
stabiliser Gx of the vertex x on the neighbourhood Δ (x) satisfies the two conditions given in …

Let Γ be a finite simple undirected graph and G≤ Aut (Γ). If G is transitive on the set of s-arcs
but not on the set of (s+ 1)-arcs of Γ, then Γ is called (G, s)-transitive. For a connected (G, s) …

The main result of this paper is that, if $\Gamma $ is a connected 4-valent $ G $-arc-
transitive graph and $ v $ is a vertex of $\Gamma $, then either $\Gamma $ is one of a well …