Loading...

Some relations between rank of a graph and its complement

Akbari, S ; Sharif University of Technology | 2007

195 Viewed
  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2006.10.025
  3. Publisher: 2007
  4. Abstract:
  5. Let G be a graph of order n and rank(G) denotes the rank of its adjacency matrix. Clearly, n ≤ rank (G) + rank (over(G, -)) ≤ 2 n. In this paper we characterize all graphs G such that rank (G) + rank (over(G, -)) = 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 (over(G, -)) = n + k. © 2006 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Integer programming ; Matrix algebra ; Adjacency matrix ; Complement of a graph ; Graph theory
  8. Source: Linear Algebra and Its Applications ; Volume 422, Issue 1 , 2007 , Pages 341-347 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0024379506004794