Generalized Quaternion Number Of Group Q <sub> 4p </ Sub> Of The Cayley Graph

In this paper, firstly, we discuss the property and the structure of group of all the automorphisms of generalized quaternion group Q4n (where n is an integer). Consequently, we show that generalized quaternion group Q4p (where p is an odd prime) has only two classes subsets whose numbers of generators are 2 by Frattini subgroup, and they are transitive under Aut(Q4p). Secondly, we investigate that the normality and regularity Cayley graphs of Q4p of valency 4 and 6. at the some time, their CI- property was still briefly illustrated.