论文信息 - Convex polyhedra of doubly stochastic matrices: II. Graph of Omegan

Convex polyhedra of doubly stochastic matrices: II. Graph of Omegan

Abstract Properties of the graph G(Ω n ) of the polytope Ω n of all n × n nonnegative doubly stochastic matrices are studied. If F is a face of Ω n which is not a k -dimensional rectangular parallelotope for k ≥ 2, then G ( F ) is Hamilton connected. Prime factor decompositions of the graphs of faces of Ω n relative to Cartesian product are investigated. In particular, if F is a face of Ω n , then the number of prime graphs in any prime factor decomposition of G ( F ) equals the number of connected components of the neighborhood of any vertex of G ( F ). Distance properties of the graphs of faces of Ω n are obtained. Faces F of Ω n for which G ( F ) is a clique of G(Ω n ) are investigated.

Richard A. Brualdi | Peter M. Gibson

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