Minimum rank of a graph over an arbitrary field

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Nathan L. Chenette
Sean V. Droms
Leslie Hogben
Rana Mikkelson
Olga Pryporova


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 ∈ Fn×n whose (i, j)th entry (for i ≠  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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