A graph Γ admitting a group H of automorphisms acting semi-regularly on the vertices with
exactly two orbits is called a bi-Cayley graph over H. This generalisation of a Cayley graph …

The well-known game of Rock–Paper–Scissors can be used as a simple model of
competition between three species. When modelled in continuous time using differential …

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 …

A graph is said to be half-arc-transitive if its automorphism group acts transitively on its
vertex set and its edge set, but not on its arc set. A graph is a weak metacirculant if it admits …

Constructing Half-Arc-Transitive Graphs of Valency Four with Prescribed Vertex Stabilizers |
Graphs and Combinatorics Skip to main content Springer Nature Link Account Menu Find a …

A connected graph whose automorphism group acts transitively on the edges and vertices,
but not on the set of ordered pairs of adjacent vertices of the graph is called half-arc …

The main result of this paper is that, if Γ is a finite connected 4-valent vertex-and edge-
transitive graph, then either Γ is part of a well-understood family of graphs, or every non …

A graph with a cyclic group of automorphisms acting semiregularly on the vertices with two
orbits is called a bi-circulant. A graph is half-arc-transitive if it is both vertex-transitive and …

A graph is half-arc-transitive if its automorphism group acts transitively on vertices and
edges, but not on arcs. Let p be a prime. A graph is called ap-graph if it is a Cayley graph of …

We prove that, if Γ is a finite connected 3-valent vertex-transitive, or 4-valent vertex-and edge-
transitive graph, then either Γ is part of a well-understood family of graphs, or every non …