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For a graph G on n vertices and a field F, the minimum rank of G over F, written as mrF(G), is the smallest possible rank over all n×n symmetric matrices over F whose (i,j)th entry (for i≠j) is nonzero whenever ij is an edge in G and is zero otherwise. The maximum nullity of G over F is MF(G)=n-mrF(G). The minimum rank problem of a graph G is to determine mrF(G) (or equivalently, MF(G)). This problem...
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