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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×n whose (i, j)th entry (for i = j) is nonzero whenever {i, j} is an edge in G and is zero otherwise. We show that the minimum rank of a tree is independent of the field. 1. Introduction. The minimum rank problem(More)
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 introduces a new graph parameter, Z(G), that is the minimum size of a zero forcing set of vertices and uses it to bound the minimum rank(More)
A sign pattern is a matrix whose entries are elements of {+, −, 0}; it describes the set of real matrices whose entries have the signs in the pattern. A graph (that allows loops but not multiple edges) describes the set of symmetric matrices having a zero-nonzero pattern of entries determined by the absence or presence of edges in the graph. DeAlba et al.(More)
New generations of neutron scattering sources and instrumentation are providing challenges in data handling for user software. Time-of-Flight instruments used at pulsed sources typically produce hundreds or thousands of channels of data for each detector segment. New instruments are being designed with thousands to hundreds of thousands of detector(More)
A sign pattern Z (a matrix whose entries are elements of {+, −, 0}) is spectrally arbitrary if for any self-conjugate spectrum there is a real matrix with sign pattern Z having the given spectrum. Spectrally arbitrary sign patterns were introduced in [5], where it was (incorrectly) stated that if a sign pattern Z is reducible and each of its irreducible(More)
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