摘要
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.
出处
《辽宁石油化工大学学报》
CAS
2008年第4期91-94,共4页
Journal of Liaoning Petrochemical University
基金
辽宁省教育厅高校科研项目(2004F100)
辽宁石油化工大学重点学科建设资助项目(K200409)。
关键词
图
补图
色数
Q谱半径
拉普拉斯谱半径
上界
Graph
Complement graph
Chromatic number
spectral radius
Laplace spectral radius
Upper bound