| Abstract: | In this paper, we give a necessary and sufficient condition for the integrality of Cayley graphs over the dihedral group (D_n=langle a,bmid a^n=b^2=1,bab=a^{-1}rangle ). Moreover, we also obtain some simple sufficient conditions for the integrality of Cayley graphs over (D_n) in terms of the Boolean algebra of (langle arangle ), from which we find infinite classes of integral Cayley graphs over (D_n). In particular, we completely determine all integral Cayley graphs over the dihedral group (D_p) for a prime p. |
