Minimum rank of a graph over an arbitrary field
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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 ∈ 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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