| 图与其补图Q谱半径之和的上界 |
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| 引用本文： | 张丽镯,宋岱才,裴芳芳.图与其补图Q谱半径之和的上界[J].辽宁石油化工大学学报,2008,28(4). |
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| 作者姓名： | 张丽镯 宋岱才 裴芳芳 |
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| 作者单位： | 辽宁石油化工大学理学院,辽宁抚顺,113001 |
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| 基金项目： | 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)。 |
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| 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。
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| 关 键 词： | 图 补图 色数 Q谱半径 拉普拉斯谱半径 上界 |
Upper Bound on the Sum of the Q Spectral Radius of a Graph and Its Complement |
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| ZHANG Li-zhuo,SONG Dai-cai,PEI Fang-fang.Upper Bound on the Sum of the Q Spectral Radius of a Graph and Its Complement[J].Journal of Liaoning University of Petroleum & Chemical Technology,2008,28(4). |
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| Authors: | ZHANG Li-zhuo SONG Dai-cai PEI Fang-fang |
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| Affiliation: | School of Sciences;Liaoning University of Petroleum & Chemical Technology;Fushun Liaoning 113001;P.R.China |
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| Abstract: | 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(G-))≤2(Δ-δ+n-1) and ρ(Q(G))+ρQ(G-))≤2n-3+(2-12)(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+(2-1k)(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. |
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| Keywords: | Graph Complement graph Chromatic number spectral radius Laplace spectral radius Upper bound |
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