| In this dissertation, the author mainly discusses the properties and the structure of Parsonsgraphs, especially discusses the problem of the maximum clique number of Parsons graPhs Tb(d,q) on the special linear group SL, (q). Firstly, using linear transformations and the conclusionsin the finite field, the author gets a lower bound on the maximum clique number mb(2' q) ofParsons graphs Tb(2, q), then on the base of it, a lower bound on mb(d, q) is given, where d>2.Secondly, the author gives some exact values of mb(2' q) for some values of b, which impliesthat the above lower bound is not only the lower bound but also the infimum. In the rest of thisdissertation, the author studies other problem about Parsons graphs Tb(d, q). The sufficientcondition is given to prove that Parsons graphs Tb(2, q) is l -- factorable. The author discussesthe directional Parsons graPhs DTb(d, q) and gives some new conclusions about them. In theend, the author brings forward some new concepts about Parsons graphs and makes someelementary discussions on them. |
