Tetravalent vertex-transitive graphs of order 4p

A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this article, the tetravalent vertex-transitive non-Cayley graphs of order 4p are classified for each prime p. As a result, there are one sporadic and five infinite families of such graphs, of which the sporadic one has order 20, and one infinite family exists for every prime p>3, two families exist if and only if p=1 (mod 8) and the other two families exist if and only if p=1 (mod 4). For each family there is a unique graph for a given order.(C)2011 Wiley Periodicals, Inc.