Abstract:

Let $p$ be an odd prime. In this paper, we obtain the number of (connected)

Cayley graphs on the dicyclic groups $T_{4p}=\langle a,b~|~a^{p}=b^4=1,b^{-1}ab=a^{-1}\rangle$ up to isomorphism by using the P\'{o}lya enumeration theorem.

Key words: Cayley graph ,  Dicyclic group , Isomorphic classes ,  P\'{o}lya enumeration theorem