A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer

A tetravalent half-arc-transitive graph with non-abelian vertex stabilizer

A construction is given of a valent arc transitive graph with vertex stabilizer isomorphic to the dihedral group D The graph has vertices and is the rst known example of a valent arc transitive graph with nonabelian vertex stabilizer A VALENT HALF ARC TRANSITIVE GRAPH

Vertex-Transitive Non-Cayley Graphs with Arbitrarily Large Vertex-Stabilizer

A construction is given for an infinite family {0n} of finite vertex-transitive non-Cayley graphs of fixed valency with the property that the order of the vertex-stabilizer in the smallest vertex-transitive group of automorphisms of 0n is a strictly increasing function of n. For each n the graph is 4-valent and arc-transitive, with automorphism group a symmetric group of large prime degree p> 2...

Tetravalent half-arc-transitive graphs of order p4

A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let p and q be primes. It is known that no tetravalent half-arc-transitive graphs of order 2p2 exist and a tetravalent half-arctransitive graph of order 4p must be non-Cayley; such a non-Cayley graph exists if and only if p − 1 is divisible by 8 and it is unique for a given o...

Quartic half-arc-transitive graphs with large vertex stabilizers

A 1 2 -arc-transitive graph is a vertexand edgebut not arc-transitive graph. In all known constructions of quartic 1 2 -arc-transitive graphs, vertex stabilizers are isomorphic to Z 2,Z 2 2 or to D8. In this article, for each positive integer m ≥ 1, an infinite family of quartic 1 2 -arctransitive graphs having vertex stabilizers isomorphic to Z m

Tetravalent half-edge-transitive graphs and non-normal Cayley graphs