科研之友
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摘要
Let S(G) denote a class of positive semipositive matrices associated with the given graph G, and msr(G) be the minimum rank of matrices among S(G). A lower bound of msr(G) given in Jiang, Mitchell and Narayan [Unitary matrix digraphs and minimum semidefinite rank, Linear Alg. Appl., 428(2008): 1685-1695] for bipartite graph is generalized, to any graph. Moreover, a method to construct an OS-vertex set is proposed.
