This thesis mainly studies NNN-graphs and NNN-properties for finite groups. We first show that applying Cartesian product, direct product and strong product respectively to an NNN-graph and finitely many normal Cayley graphs construct new NNN-graphs. Next we solve the NNN-property for simple groups, (Z2)d, and Zn where n is not divisible by 8. We classify the regular subgroups of Hoi(Z2k) and solve the NNN-property for Z2k with k less than or equal to 6. In this thesis, we also study 2-arc transltive covers of hypercubes and construct new 2-arc-transitive graphs which are normal Cayley graphs.
|Qualification||Doctor of Philosophy|
|Award date||31 Dec 2018|
|Publication status||Unpublished - 2018|