Some relations between rank of a graph and its complement

被引：0
|
作者：
Akbari, Saieed
Alipour, Alireza
Boroojeni, Javad Ebrahimi
Ghorbani, Ebrahim
Shirazi, Mirhamed Mirjalalieh
机构：
[1] Sharif Univ Technol, Dept Math Sci, Tehran, Iran
[2] Inst Studies Theoret Phys & Math, Tehran, Iran
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2007年 / 422卷 / 01期
关键词：
adjacency matrix; rank; complement of a graph;
D O I：
10.1016/j.laa.2006.10.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a graph of order n and rank (G) denotes the rank of its adjacency matrix. Clearly, n <= rank (G) + rank ((G) over bar) <= 2n. In this paper we characterize all graphs G such that rank (G) + rank ((G) over bar) = n, n + 1 or n + 2. Also for every integer n >= 5 and any k, 0 <= k <= n, we construct a graph G of order n, such that rank(G) + rank((G) over bar) = n + k. (c) 2006 Elsevier Inc. All rights reserved.
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页码：341 / 347
页数：7
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