Let G be a simple graph with n vertices, the new upper bound on the sum of the Q spectral radius of a graph and its complement were given by its m edges, minimal degree of a vertex δ, maximal degree of a vertex Δ and chromatic number k． When graph G has no isolated vertex ,we have 2(n-1)≤ρ(Q(G))+ρ(Q([AKG-]))≤2(Δ-δ+n-1) and ρ(Q(G))+ρQ([AKG-]))≤2n-3+[KF(][JB((]2-[SX(]1[]2[SX)][JB))](n-1)n[KF)]，where t=min{k,[AKk-]}. When graph [AKG-] has l isolated vertices ,we have ρ(Q(G))+ρ(Q([AKG-]))≤2n-3+[KF(][JB((]2-[SX(]1[]k[SX)][JB))](n-1)2+l[KF)]. At the same time the upper bound on the sum of the Laplace spectral radius of a graph and its complement was given.

Let G be a simple graph with n vertices and ρ(G) be its spectral radius．Let [AKG-] be the complement [KG*3]graph [KG*3]of [KG*3]G, [KG*3]and ρ([AKG-]) be the spectral radius of [AKG-]．The upper bound on sum of the spectral radius of G and [AKG-] were given, and the upper bound on sum of the spectral radius of G and [AKG-] were given when G be unconnected and [AKG-] be connected .