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Expected values of parameters associated with the minimum rank of a graph

โœ Scribed by H. Tracy Hall; Leslie Hogben; Ryan Martin; Bryan Shader

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
272 KB
Volume
433
Category
Article
ISSN
0024-3795

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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 min

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For a simple graph G on n vertices, the minimum rank of G over a field F, written as mr F (G), is defined to be the smallest possible rank among all n ร— n symmetric matrices over F whose (i, j)th entry (for i / = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. A symmetric integ