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https://www.um.edu.mt/library/oar/handle/123456789/29143| Title: | Zero forcing sets and the minimum rank of graphs |
| Authors: | Barioli, Francesco Barrett, Wayne Butler, Steve Cioaba, Sebastian M. Cvetkovic, Dragos Fallat, Shaun M. Godsil, Chris Haemers, Willem Hogben, Leslie Mikkelson, Rana Narayan, Sivaram Pryporova, Olga Sciriha, Irene So, Wasin Stevanovic, Dragan Holst van der, Hein Meulen Vander, Kevin Wangsness Wehe, Amy |
| Authors: | AIM Minimum Rank – Special Graphs Work Group |
| Keywords: | Symmetric operators Matrices Mathematics -- Problems, exercises, etc |
| Issue Date: | 2008 |
| Publisher: | Elsevier Inc. |
| Citation: | AIM Minimum Rank – Special Graphs Work Group. (2008). Zero forcing sets and the minimum rank of graphs. Linear Algebra and its Applications, 428(7), 1628-1648. |
| 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 ) is nonzero whenever is an edge in G and is zero otherwise. This paper introduces a new graph parameter, , 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. |
| URI: | https://www.um.edu.mt/library/oar//handle/123456789/29143 |
| Appears in Collections: | Scholarly Works - FacSciMat |
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| File | Description | Size | Format | |
|---|---|---|---|---|
| Zero_forcing_sets_and_the_minimum_rank_of_graphs_2008.pdf Restricted Access | 239.7 kB | Adobe PDF | View/Open Request a copy |
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