An infinite family of cubic edge- but not vertex-transitive graphs

An infinite family of cubic edge- but not vertex-transitive graphs

Constructing Cubic Edge-but Not Vertex-transitive Graphs

Slovenija Abstract An innnite family of cubic edge-transitive but not vertex-transitive graph graphs with edge stabilizer isomorphic to Z Z 2 is constructed.

Constructing cubic edge- but not vertex-transitive graphs

An in nite family of cubic edge transitive but not vertex transitive graph graphs with edge stabilizer isomorphic to Z is constructed

An infinite series of regular edge- but not vertex-transitive graphs

Let n be an integer and q be a prime power. Then for any 3 ≤ n ≤ q − 1, or n = 2 and q odd, we construct a connected q-regular edgebut not vertextransitive graph of order 2qn+1. This graph is defined via a system of equations over the finite field of q elements. For n = 2 and q = 3, our graph is isomorphic to the Gray graph.

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.