On Cubic Symmetric Graphs Of Order 4p~n

A graph is said to be symmetric if its automorphism group acts transitively on its arcs. Let p be a prime. In the thesis, we aim to investigate the cubic symmetric graph of order 4pn with n a positive integer. In [J. Combin. Theory B,97 (2007) 627-646.], by using graph covering theory, Feng and Kwak have classified cubic symmetric graphs of order 4p2. In this thesis, we give a new proof of this result by analyzing the automorphism groups of graphs. Recently, in [Ars Combin., in press.], Zhou classified cubic symmetric graph of order 4p3, and in this thesis, we give a characterization of cubic symmetric graphs of order 4p4. As a result, we know that such graph exist only when p= 2,5 or 7. Also, the classification of cubic symmetric Cayley graphs of order 4p4 is given. At last, we prove that if p≠5,7 then every cubic symmetric graph of order 4pn is a Cayley graph.