Pq And Order Non-orientable Regular Map And A Small Second-order Pairs Of Primitive And Semi-symmetric Graph Classification,

The thesis consists of two parts.The first part deals with classification of regular maps. A map on a surface is a cellular decomposition of closed surface into O-cells called vertices, 1-cells called edges and 2-cells called faces. The vertices and edges of a map form its underlying graph. A map is said to be orientable if the supporting surface is orientable. Otherwise, said to be non-orientable. By an automorphism of a map M, we mean an automorphism of underlying graph X which can be extended to an orientation preserving self-homeomorphism of surface. The set of automorphism forms a group, called the automorphism group Aut(M) of the map M. For combinatorial oriented map M, Aut(M) acts semi-regularly on the arcs of X. If it acts regularly, we call the map as well as the corresponding embedding regular. For combinatorial unoriented map M, Aut(M) acts semi-regularly on the flags of X. If it acts regularly, we call the map as well as the corresponding embedding regular.In the first part, we classify the non-orientable regular embeddings of connected graphs of order pq for any two distinct primes p and q into non-orientable surface. With the result of classification of the orientable regular embeddings of connected graphs of order pq, we obtained all regular maps with underlying graph of order pq for any two distinct primes p and q.The second part deals with classification of biprimitive semisymmetric graphs. A regular edge-transitive graph which is not vertex-transitive is said to be se(?)isymmetric. Every semisymmetric graph X is necessarily bipartite, the two parts having equal size, and the automorphism group Aut(X) acting transitively on each of these...