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Minimum rank of a graph

In mathematics, the minimum rank is a graph parameter for any graph G. It was motivated by the Colin de Verdière's invariant.
Wikipedia

Related topics

Related topics

9 relations
Adjacency matrixColin de Verdière graph invariantConnected component (graph theory)Graph (discrete mathematics)
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Broader (1)

Algebraic graph theory

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
2019
2019
Critical ideals, minimum rank and zero forcing number
There are profound relations between the zero forcing number and minimum rank of a graph. We study the relation of both… Expand
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2019
2019
Minimum rank and zero forcing number for butterfly networks
Zero forcing is a graph propagation process introduced in quantum physics and theoretical computer science, and closely related… Expand
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2018
2018
Diagonal entry restrictions in minimum rank matrices Wayne
Let F be a field, let G be a simple graph on n vertices, and let S (G) be the class of all F -valued symmetric n × n matrices… Expand
2016
2016
Approximating the minimum rank of a graph via alternating projection
The minimum rank problem asks to find the minimum rank over all matrices with a given pattern associated with a graph. This… Expand
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Review
2014
Review
2014
Minimum Rank, Maximum Nullity, and Zero Forcing Number of Graphs
This chapter represents an overview of research related to a notion of the “rank of a graph" and the dual concept known as the… Expand
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2013
2013
The Minimum Rank Problem for Outerplanar Graphs
The Minimum Rank Problem for Outerplanar Graphs John H. Sinkovic III Department of Mathematics, BYU Doctor of Philosophy Given a… Expand
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2011
2011
The Minimum Rank of Universal Adjacency Matrices
Abstract In this paper we introduce a new parameter for a graph called the minimum universal rank. This parameter is similar to… Expand
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2010
2010
On the minimum rank of a graph over finite fields
In this paper we deal with two aspects of the minimum rank of a simple undirected graph $G$ on $n$ vertices over a finite field… Expand
2008
2008
Program for calculating bounds on the minimum rank of a graph using Sage
The minimum rank of a simple graph $G$ is defined to be the smallest possible rank over all symmetric real matrices whose $ij$th… Expand
2007
2007
Minimum rank of a graph over an arbitrary field
For a field F and graph G of order n, the minimum rank of G over F is defined to be the smallest possible rank over all symmetric… Expand
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