Abstract: 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 .

Key words: Graph, Complement graph, Connected graph, Spectral radius, Upper bound 

摘要： 设G为n阶简单图，ρ(G)是G的谱半径,图G的补图记作[AKG-],[AKG-]的谱半径记作ρ([AKG-])。给出了简单图及其补图谱半径之和ρ(G)+ρ([AKG-])的上界，以及当图G不连通但其补图[AKG-]是连通图时ρ(G)+ρ([AKG-])的上界。

关键词: 图, 补图, 连通图, 谱半径, 上界