Vertex-transitive Graphs Which Are Not Cayley Graphs

  title={Vertex-transitive Graphs Which Are Not Cayley Graphs},
  author={Brendan D. McKay}
The Petersen graph on 10 vertices is the smallest example of a vertex-transitive graph which is not a Cayley graph. We consider the problem of what orders such graphs have. In this, the first of a series of papers, we present a sequence of constructions which solve the problem for many orders. In particular, such graphs exist for all orders divisible by a fourth power, and all even orders which are divisible by a square. 


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