Eigenvalue problems of Nordhaus-Gaddum type

被引：24
|
作者：
Nikiforov, Vladimir [1 ]
机构：
[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA
来源：
DISCRETE MATHEMATICS | 2007年 / 307卷 / 06期
关键词：
graph eigenvalues; complementary graph; maximum eigenvalue; minimum eigenvalue; Nordhaus-Gaddum problems;
D O I：
10.1016/j.disc.2006.07.035
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let G be a graph with n vertices and in edges and let mu(1) (G) >= ... >= (G) be the eigenvalues of its adjacency matrix. We discuss the following general problem. For k fixed and n large, find or estimate f(k)(n) = max(nu(G)=n)vertical bar mu(k)(G)vertical bar+vertical bar mu(k)((G) over bar) In particular, we prove that (4)/(3)n - 2 <= f(1) (n) < (root 2 - c)n for some c > 10(-7) independent of n. We also show that (root 2)/(2)n - 3 < f(2)(n) < (root 2)/(2) n, (root 2)/(2)n - 3 < f(2)(n) < (root 3)/(2) n, (c) 2006 Elsevier B.V. All rights reserved.
引用
收藏
页码：774 / 780
页数：7
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