Thumbnail Image
Item

Zero forcing sets and minimum rank of graphs

Barioli,Francesco
; 
Barrett,Wayne
; 
Butler,Steve
; 
Cioabǎ,S.M.
; 
Cvetković,D.
; 
Fallat,Shaun M.
; 
Godsil,Chris D.
; 
Haemers,W.H.
; 
Hogben,Leslie
; 
Mikkelson,Rana
... show 8 more
Abstract
The minimum rank of a simple graph G is defined to be the smallest possible rank over all symmetric real matrices whose ijth entry (for i /= j ) is nonzero whenever {i, j } is an edge in G and is zero otherwise. This paper introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices and uses it to bound the minimum rank for numerous families of graphs, often enabling computation of the minimum rank.
Description
Date
2008
Journal Title
Journal ISSN
Volume Title
Publisher
Collections
Tilburg University Research Output Collection
Show all metadata
Files
Thumbnail Image
1-s2.0-S0024379507004624-main.pdf
Adobe PDF, 235.51 KB
Research Projects
Organizational Units
Journal Issue
Keywords
minimum rank, rank, graph, symmetric matrix, matrix
Citation
Barioli, F, Barrett, W, Butler, S, Cioabǎ, S M, Cvetković, D, Fallat, S M, Godsil, C D, Haemers, W H, Hogben, L, Mikkelson, R, Narayan, S K, Pryporova, O, Sciriha, I, So, W, Stevanovic, D, van der Holst, H, Vander Meulen, K & Wangsness Wehe, A 2008, 'Zero forcing sets and minimum rank of graphs', Linear Algebra and its Applications, vol. 428, no. 7, pp. 1628-1648.
URI
https://hdl.handle.net/20.500.14602/49629
License
info:eu-repo/semantics/openAccess
Embedded videos