A note on doubly stochastic graph matrices

A note on doubly stochastic graph matrices

A sharp lower bound for the smallest entries, among those corresponding to edges, of doubly stochastic matrices of trees is obtained, and the trees that attain this bound are characterized. This result is used to provide a negative answer to Merris’ question in [R. Merris, Doubly stochastic graph matrices II, Linear Multilin. Algebra 45 (1998) 275–285]. © 2005 Elsevier Inc. All rights reserved....

Vertex degrees and doubly stochastic graph matrices

In this article, the relationship between vertex degrees and entries of the doubly stochastic graph matrix has been investigated. In particular, we present an upper bound for the main diagonal entries of a doubly stochastic graphmatrix and investigate the relations between a kind of distance for graph vertices and the vertex degrees. These results are used to answer in negative Merris’ question...

On a Conjecture concerning Doubly Stochastic Matrices

On A Conjecture Concerning Doubly Stochastic Matrices

In a 2002 paper, Kirkland showed that if T ∈ Rn×n is an irreducible stochastic matrix with stationary distribution vector πT , then for A = I − T , maxj=1,...,n πj‖A j ‖∞ ≥ n−1 n , where Aj , j = 1, . . . , n, are the (n − 1) × (n − 1) principal submatrices of A obtained by deleting the j–th row and column of A. He also conjectured that equality holds in that lower bound if and only if either T...

On Doubly Stochastic Graph Optimization

In this paper we introduce an approximate optimization framework for solving graphs problems involving doubly stochastic matrices. This is achieved by using a low dimensional formulation of the matrices and the approximate solution is achieved by a simple subgradient method. We also describe one problem that can be solved using our method.