Biprimitive Semisymmetric Graphs From PSL (2,p) And Regular Coverings Of Cube

This thesis consists of two parts. The first part deals with the construction of semisymmetric graphs and the second part classifies the edge-transitive regular coverings of the cube, whose covering transformation groups are iso-morphic to the elementary abelian p-groups.A regular and edge-transitive graph which is not vertex-transitive is said to be semisymmetric. It is easy to see that every semisymmetric graph is necessarily bipartite, with the two parts having equal size and che automorphism group acting transitively on each of these two parts. A semisymmetric graph is called biprimitive if its automorphism group acts primitively on each part. This thesis will give a classification of biprimitive semisymmetric graphs arising from the action of the group PSX(2,p), where p=+1 (mod 10) a prime, on cosets of A5. By the way, the structure of the suborbits of PGL(2,p) on the cosets of A5 is determined.For a given finite connected graph F, a group H of automorphisms of F and a finite group A = Z, Du, Kawk and Xu (see [6]) get some new matrix-theoretical characterizations to classify all the connected regular coverings of F having A as its covering transformation group, on which each automorphism in H can be lifted . With this method, in the present thesis, we will classify all the connected regular covering graphs of the cube satisfying the following two properties: (1) the covering transformation group is isomorphic to the elementary abelian p-group; (2) the group of fibre-preserving automorphisms acts edge-transitively.