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.

引用

页码：341 / 347

页数：7

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