Nowhere-zero 3-flows in graphs admitting solvable arc-transitive groups of automorphisms

On Cubic Graphs Admitting an Edge-Transitive Solvable Group

Using covering graph techniques, a structural result about connected cubic simple graphs admitting an edge-transitive solvable group of automorphisms is proved. This implies, among other, that every such graph can be obtained from either the 3-dipole Dip3 or the complete graph K4, by a sequence of elementary-abelian covers. Another consequence of the main structural result is that the action of...

An infinite family of biquasiprimitive 2-arc transitive cubic graphs

A new infinite family of bipartite cubic 3-arc transitive graphs is constructed and studied. They provide the first known examples admitting a 2-arc transitive vertex-biquasiprimitive group of automorphisms for which the stabiliser of the biparts is not quasiprimitive on either bipart.

A census of 4-valent half-arc-transitive graphs and arc- transitive digraphs of valence two

A complete list of all connected arc-transitive asymmetric digraphs of in-valence and out-valence 2 on up to 1000 vertices is presented. As a byproduct, a complete list of all connected 4-valent graphs admitting a 12 -arc-transitive group of automorphisms on up to 1000 vertices is obtained. Several graph-theoretical properties of the elements of our census are calculated and discussed.

A Family of Non-quasiprimitive Graphs Admitting a Quasiprimitive 2-arc Transitive Group Action

Let 0 be a simple graph and let G be a group of automorphisms of 0. The graph is (G, 2)-arc transitive if G is transitive on the set of the 2-arcs of 0. In this paper we construct a new family of (PSU(3, q2), 2)-arc transitive graphs 0 of valency 9 such that Aut0 = Z3.G, for some almost simple group G with socle PSU(3, q2). This gives a new infinite family of non-quasiprimitive almost simple gr...

Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms