Convex polyhedra of doubly stochastic matrices: II. Graph of |
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Authors: | Richard A Brualdi Peter M Gibson |
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Affiliation: | University of Wisconsin, Madison, Wisconsin 53706 USA;University of Alabama in Huntsville, Huntsville, Alabama 35807 USA |
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Abstract: | Properties of the graph of the polytope of all n × n nonnegative doubly stochastic matrices are studied. If is a face of which is not a k-dimensional rectangular parallelotope for k ≥ 2, then G() is Hamilton connected. Prime factor decompositions of the graphs of faces of relative to Cartesian product are investigated. In particular, if is a face of , then the number of prime graphs in any prime factor decomposition of G() equals the number of connected components of the neighborhood of any vertex of G(). Distance properties of the graphs of faces of are obtained. Faces of for which G() is a clique of are investigated. |
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