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 doubly stochastic graph matrices. These results may also be used to establish relations between graph structure and entries of doubly stochastic graph matrices. 2010 Wiley Periodicals, Inc. J Graph Theory 66: 104–114, 2011 Contract grant sponsor: National Natural Science Foundation of China; Contract grant numbers: 10971137; 10531070; Contract grant sponsor: National Basic Research Program (973) of China; Contract grant number: 2006CB805900; Contract grant sponsor: National High Technology Research and Development Program (863) of China; Contract grant number: 2006AA11Z209; Contract grant sponsor: Science and Technology Commission of Shanghai Municipality; Contract grant number: 09XD1402500. Journal of Graph Theory 2010 Wiley Periodicals, Inc.