A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. In this
paper, the s-regular elementary abelian coverings of the complete bipartite graph K3, 3 and …

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 …

A list is given of all semisymmetric (edge-but not vertex-transitive) connected finite cubic
graphs of order up to 768. This list was determined by the authors using Goldschmidt's …

A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-
regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte (1947, 1959) …

Quite a lot of attention has been paid recently to the construction of edge-or arc-transitive
covers of symmetric graphs. In most cases, the approach has involved voltage graph …

This is the first in the series of articles stemming from a systematical investigation of finite
edge-transitive tetravalent graphs, undertaken recently by the authors. In this article, we …

We introduce the notion of the k-closure of a group of automorphisms of a locally finite tree,
and give several examples of the construction. We show that the k-closure satisfies a new …

A complete classification of cubic symmetric graphs of girth 6 is given. It is shown that with
the exception of the Heawood graph, the Moebius–Kantor graph, the Pappus graph, and the …

A graph Γ is symmetric if its automorphism group acts transitively on the arcs of Γ, and s-
regular if its automorphism group acts regularly on the set of s-arcs of Γ. Tutte [WT Tutte, A …

This paper deals with graphs the automorphism groups of which are transitive on vertices
and on undirected paths (but not necessarily on directed walks) of some fixed length. In …