Combinatorial Matrix Classes

  title={Combinatorial Matrix Classes},
  author={Richard A. Brualdi},
1. Introduction 2. Basic existence theorems for matrices with prescribed properties 3. The class A(R S) of (0,1)-matrices 4. More on the class A(R S) of (0,1)-matrices 5. The class T(R) of tournament matrices 6. Interchange graphs 7. Classes of symmetric integral matrices 8. Convex polytopes of matrices 9. Doubly stochastic matrices. 

Combinatorial Matrix Theory

This chapter discusses theorems for combinatorially constrained matrices, and some special graphs found in the literature on matrix algebra and digraphs.

An extension of the polytope of doubly stochastic matrices

We consider a class of matrices whose row and column sum vectors are majorized by given vectors b and c, and whose entries lie in the interval [0, 1]. This class generalizes the class of doubly

Majorization classes of integral matrices

Zero-one completely positive matrices and the A(R, S) classes

Abstract A matrix of the form A = BBT where B is nonnegative is called completely positive (CP). Berman and Xu (2005) investigated a subclass of CP-matrices, called f0, 1g-completely positive

Majorization for (0,1)-matrices

L-rays of permutation matrices and doubly stochastic matrices

Orthogonal symmetric matrices and joins of graphs

Extremal matrices for the Bruhat-graph order

We consider the class of symmetric -matrices with zero trace and constant row sums k which can be identified with the class of the adjacency matrices of k-regular undirected graphs. In a previous


Abstract We investigate the number of symmetric matrices of nonnegative integers with zero diagonal such that each row sum is the same. Equivalently, these are zero-diagonal symmetric contingency