Minimum rank of a tree over an arbitrary field

Date
2007-07-01
Authors
Chenette, Nathan
Droms, Sean
Hogben, Leslie
Mikkelson, Rana
Pryporova, Olga
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Mathematics
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Abstract

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 matrices A. F-n x n whose (i, j) th entry (for i not equal j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. It is shown that the minimum rank of a tree is independent of the field.

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This article is published as Chenette, Nathan, Sean Droms, Leslie Hogben, Rana Mikkelson, and Olga Pryporova. "Minimum rank of a tree over an arbitrary field." The Electronic Journal of Linear Algebra 16 (2007): 183-186. DOI: 10.13001/1081-3810.1193. Posted with permission.

Keywords
Minimum rank, Tree, Graph, Field, Path, Symmetric matrix
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