Variants on the minimum rank problem: A survey II

S Fallat, L Hogben - arXiv preprint arXiv:1102.5142, 2011 - arxiv.org
The minimum rank problem for a (simple) graph $ G $ is to determine the smallest possible
rank over all real symmetric matrices whose $ ij $ th entry (for $ i\neq j $) is nonzero …

On the minimum rank of not necessarily symmetric matrices: a preliminary study

F Barioli, SM Fallat, HT Hall, D Hershkowitz… - Electronic Journal of …, 2009 - research.tue.nl
The minimum rank of a directed graph G is defined to be the smallest possible rank over all
real matrices whose ijth entry is nonzero whenever (i, j) is an arc in G and is zero otherwise …

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 …

The failed zero forcing number of a graph

K Fetcie, B Jacob, D Saavedra - Involve, a Journal of Mathematics, 2014 - msp.org
Given a graph G, the zero forcing number of G, Z (G), is the smallest cardinality of any set S
of vertices on which repeated applications of the color change rule results in all vertices …

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 …

Minimum rank, maximum nullity and zero forcing number for selected graph families

E Almodovar, L DeLoss, L Hogben, K Hogenson… - Involve, a Journal of …, 2011 - msp.org
The minimum rank of a simple graph G is defined to be the smallest possible rank over all
symmetric real matrices whose i j-th entry (for i≠ j) is nonzero whenever {i, j} is an edge in G …

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] Topics in combinatorial matrix theory

M Tréfois - 2016 - core.ac.uk
In the finite-time average consensus problem, the goal is to make the agents meet at the
average of their initial positions in a finite number of steps, with the constraint that each …

[PDF][PDF] Applications of zero forcing number to the minimum rank problem

CH Lin - 2011 - www-math.nsysu.edu.tw
The minimum rank problem of a graph G is to determine the smallest rank over all real
symmetric matrices whose ij-entry, i≠ j, is nonzero whenever ij is an edge and is zero …

[PDF][PDF] inv lve

E Almodovar, L DeLoss, L Hogben, K Hogenson… - academia.edu
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= j) is nonzero whenever {i, j} is an edge in G …