Abstract
We consider the convex polytope S n(x) that consist of those n× n (row) stochastic matrices having a common nonnegative (left) fixed vector x t. We examine the 1-skeleton of S n(x) and show how to construct all extreme points adjacent to a given one (as vertices of the 1-skeleton). Connections with transportation polytopes are discussed. Further, we give a formula for the degree of an extreme point in the 1-skeleton of S n(x) , find its maximum and minimum values, and determine when all degrees are equal. An explicit description of the 1-skeleton is given for n=3.
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