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

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 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

Strongly regular edge-transitive graphs

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...