15 research outputs found
Locally arc-transitive graphs of valence with trivial edge kernel
In this paper we consider connected locally -arc-transitive graphs with
vertices of valence 3 and 4, such that the kernel of the action
of an edge-stabiliser on the neighourhood is
trivial. We find nineteen finitely presented groups with the property that any
such group is a quotient of one of these groups. As an application, we
enumerate all connected locally arc-transitive graphs of valence on at
most 350 vertices whose automorphism group contains a locally arc-transitive
subgroup with
Edge-transitive regular Zn-covers of the Heawood graph
AbstractA regular cover of a graph is said to be an edge-transitive cover if the fibre-preserving automorphism subgroup acts edge-transitively on the covering graph. In this paper we classify edge-transitive regular Zn-covers of the Heawood graph, and obtain a new infinite family of one-regular cubic graphs. Also, as an application of the classification of edge-transitive regular Zn-covers of the Heawood graph, we prove that any bipartite edge-transitive cubic graph of order 14p is isomorphic to a normal Cayley graph of dihedral group if the prime p>13
Recent trends and future directions in vertex-transitive graphs
A graph is said to be vertex-transitive if its automorphism group acts transitively on the vertex set. Some recent developments and possible future directions regarding two famous open problems, asking about existence of Hamilton paths and existence of semiregular automorphisms in vertex-transitive graphs, are discussed, together with some recent results on arc-transitive graphs and half-arc-transitive graphs, two special classes of vertex-transitive graphs that have received particular attention over the last decade