Computational and theoretical challenges for computing the minimum rank of a graph

IV Hicks, B Brimkov, L Deaett, R Haas… - INFORMS Journal …, 2022 - pubsonline.informs.org
The minimum rank of a graph G is the minimum of the ranks of all symmetric adjacency
matrices of G. We present a new combinatorial bound for the minimum rank of an arbitrary …

Techniques for determining the minimum rank of a small graph

L DeLoss, J Grout, L Hogben, T McKay, J Smith… - Linear Algebra and its …, 2010 - Elsevier
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 …

Program for calculating bounds on the minimum rank of a graph using Sage

L DeLoss, J Grout, T McKay, J Smith, G Tims - arXiv preprint arXiv …, 2008 - arxiv.org
The minimum rank of a simple graph $ G $ is defined to be the smallest possible rank over
all symmetric real matrices whose $ ij $ th entry (for $ i\neq j $) is nonzero whenever $\{i, j\} …

An exact algorithm for the minimum rank of a graph

B Brimkov, Z Scherr - arXiv preprint arXiv:1912.00158, 2019 - arxiv.org
The minimum rank of a graph G is the minimum rank over all real symmetric matrices whose
off-diagonal sparsity pattern is the same as that of the adjacency matrix of G. In this note we …

[PDF][PDF] Minimum rank of graphs powers family

AM Nazari, MK Radpoor - Open Journal of Discrete Mathematics, 2012 - researchgate.net
Minimum Rank of Graphs Powers Family Page 1 Open Journal of Discrete Mathematics,
2012, 2, 65-69 doi:10.4236/ojdm.2012.22012 Published Online April 2012 (http://www.SciRP.org/journal/ojdm) …

[HTML][HTML] Minimum Rank of Graphs Powers Family

N Alimohammad M, R Marzieh Karimi - Open Journal of Discrete …, 2012 - scirp.org
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Books Conferences News About Us Jobs Open Journal of Discrete Mathematics Vol.2 No.2(2012) …