图与其补图Q谱半径之和的上界

Upper Bound on the Sum of the Q Spectral Radius of a Graph and Its Complement

设G为n阶简单图,利用边数m,最小、最大顶点度δ和Δ以及色数k给出了G与其补图-G的Q谱半径之和的上界,当G不含孤立点时有:2(n-1)≤ρ(Q(G))+ρ(Q(-G))≤2(Δ-δ+n-1)和ρ(Q(G))+ρQ(-G))≤2n-3+2-12(n-1)n,其中t=min{k,-k}。当-G含l个孤立点时有:ρ(Q(G))+ρ(Q(-G))≤2n-3+2-1k(n-1)2+l,同时给出了图G与其补图-G的拉普拉斯谱半径之和的一个上界。

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 A and chromatic number k. When graph G has no isolated vertex ,we have 2（n-2）≤ρ（Q（G））＋ρ（Q（G））≤2（△-δ＋n-1） and ρ（Q（G））＋ρQ（G^-））≤2n-3＋√（2-1/2）（n-1）n where t=min{k,k^-}. When graph G has l isolated vertices ,we have ρ（Q（G））＋ρ（Q（G^-））≤2n-3＋√（2-1/k）（n-1）^2＋l.At the same time the upper bound on the sum of the Laplace spectral radius of a graph and its complement was given.