Let Ξ=Cay(Znβ,Skβ) be the Cayley graph on the cyclic additive group Znβ(nβ₯4), where S1β={1,nβ1}, \dots , Skβ=Skβ1ββͺ{k,nβk} are the inverse-closed subsets of Znββ{0} for any kβN, 1β€kβ€[2nβ]β1. In this paper, we will show that Ο(Ξ)=Ο(Ξ)=k+1 if and only if k+1β£n. Also, we will show that if n is an even integer and k=2nββ1 then Aut(Ξ)β Z2βwrIβSym(k+1) where I={1,β¦,k+1} and in this case, we show that Ξ is an integral graph