Browsing by Author "Hedrick, Mark Blondeau"
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Item Nearly reducible and nearly decomposable - special classes of irreducible and fully indecomposable matrices(1972) Hedrick, Mark Blondeau; Sinkhorn, Richard; Baldwin, Joseph G.; Wright, Martin; Rodriguez, Dennis M.; Rhodes, Benjamin T., Jr.The purpose of this dissertation is to examine the structural properties of matrices whose entries are either 0 or 1. There are three main results. In Theorem 1, the author shows that the maximal number of positive entries (arcs) in an n x n nearly reducible matrix (minimally connected graph with n vertices) is 2(n - 1) and the matrix has a canonical form. In Theorem 2, he argues that the maximal number of positive entries in a nearly decomposable n x n matrix is 3(n - 1) and is obtained uniquely at a canonical matrix. In Theorem 3, he examines the structure of those nearly decomposable (0,l)-matrices whose permanent equals [sigma](A) - 2n + 2 where [sigma](A) is the number of positive entries in A.