On the spectrum of a class of distance-transitive graphs - Seyed Morteza Mirafzal; Ali Zafari (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2017)
Let Γ=Cay(Z_n, S_k) be the Cayley graph on the cyclic additive group Z_n (n≥ 4), where S_1={1, n-1}, … , S_k=S_ k-1{k, n-k} are the inverse-closed subsets of Z_n-{0} for any kN, 1≤ k≤ [n2]-1. In this paper, we will show that χ(Γ) = ω(Γ)=k+1 if and only if k+1|n. Also, we will show that if n is an even integer and k=n2-1 then Aut(Γ)Z_2 wr_I Sym(k+1) where I={1, … , k+1} and in this case, we show that Γ is an integral graph.