The minimum rank of symmetric matrices described by a graph: A survey

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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 surveys the current state of knowledge on the problem of determining the minimum rank of a graph and related issues. © 2007 Elsevier Inc. All rights reserved.

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Fallat, S. M., & Hogben, L. (2007). The minimum rank of symmetric matrices described by a graph: A survey. Linear Algebra and Its Applications, 426(2–3), 558–582. https://doi.org/10.1016/j.laa.2007.05.036

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