The Graphical Representations Of Connected Cubic Arc-Transitive Coset Graphs Of Minimum Degree On Projective Special Linear Group PSL(2,p)

The symmetry of graphs has been being a very hot issue in studing the group and graph and it is mainly described by some transitive properties of acting by their automorphism groups. The Cayley graph and the Sabidussi coset graph are two classical representations for these graphs. In fact, researching the symmetry of Sabidussi coset graphs has more general significance than doing so for the Cayley graph because every vertex-transitive graph is always some coset graph of its full automorphism group. We also define the normality for a coset graph like for a Cayley graph and even define a coset graph to be a graphical representation (GR in short) of a group.Depending on Sabidussi coset graphs and their normalities we have the following theorems as the main results of this thesis.1. The finite nonabelian simple group PSL(2,11) has the minimum degree 110 GR of connected cubic arc-transitive coset graphs.2. The finite nonabelian simple group PSL(2,13) has the minimum degree 182 GR of connected cubic arc-transitive coset graphs.3. The finite nonabelian simple group PSL(2,17) has the minimum degree 102 GR of connected cubic arc-transitive coset graphs.4. The finite nonabelian simple group PSL(2,23) has the minimum degree 506 GR of connected cubic arc-transitive coset graphs.The method used in this thesis is mainly group-theoretic. For concepts of group theory and algebraic graph theory we refer readers to [1, 2, 3].