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155. The proportion of various graphs in graph-designs

Author

Brualdi, Richard A., Wilson, Richard M., Brualdi, Richard A., and Wilson, Richard M.

Abstract

Let G be a family of simple graphs. A G-design on n points is a decomposition of the edges of K_n into copies of graphs in G. In case that G consists of complete graphs K_k with k in some set K of positive integers, such a G-design is called a pairwise balanced design (PBD) on n points with block sizes from K. Here we are concerned with the possible proportions of the numbers of copies of graphs G ∈ G that appear in decompositions for large n. We extend a result of Colbourn and Rodl on PBDs to G-designs, and give a further result on the possible numbers of copies of G in a G-design containing each vertex of the complete graph K_n.

Published
2010

156. Totally Nonnegative (0, 1)-Matrices

Author

Brualdi, Richard A., Kirkland, Steve, Brualdi, Richard A., and Kirkland, Steve

Abstract

We investigate (0, 1)-matrices which are totally nonnegative and therefore which have all of their eigenvalues equal to nonnegative real numbers. Such matrices are characterized by four forbidden submatrices (of orders 2 and 3). We show that the maximum number of 0s in an irreducible (0, 1)-matrix of order n is (n − 1)2 and characterize those matrices with this number of 0s. We also show that the minimum Perron value of an irreducible, totally nonnegative (0, 1)-matrix of order n equals 2 + 2 cos (2∏/n+2) and characterize those matrices with this Perron value.

Published
2010

157. Preface

Author

Böttcher, Albrecht, primary, Brualdi, Richard, additional, Dym, Harry, additional, Kaashoek, Rien, additional, and Ran, Andre, additional

Published
2013
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158. Preface

Author

Barrett, Wayne, primary, Brualdi, Richard A., additional, Shaked-Monderer, Naomi, additional, and Tadmor, Eitan, additional

Published
2013
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161. From the editor-in-chief

Author

Brualdi, Richard A.

Subjects
Numerical Analysis, Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
Published
1997
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163. From the Editor-in-Chief

Author

Brualdi, Richard A

Subjects
Numerical Analysis, Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
Published
2004
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167. WITHDRAWN: Dedication

Author

Brualdi, Richard A., primary, Laffey, Thomas J., additional, de Sá, Eduardo Marques, additional, Pate, Thomas H., additional, and Queiró, Joào, additional

Published
2011
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176. Preface

Author

Brualdi, Richard, primary, Khosrovshahi, Reza, additional, Mohar, Bojan, additional, and Rowlinson, Peter, additional

Published
2008
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181. Nearly symmetric-indecomposable matrices.

Author

Berliner, Adam H. and Brualdi, Richard A.

Subjects
*SYMMETRY, *INDECOMPOSABLE modules, *MATRICES (Mathematics), *GRAPH theory, *MATHEMATICAL models
Abstract

We introduce nearly symmetric-decomposable matrices, which are a symmetric analogue of nearly decomposable matrices. The defining matrix property is related to 2-matching covered and minimally 2-matching covered properties of a graph (possibly containing loops). We develop constructions and properties of nearly symmetric-decomposable-matrices, some of which relate to the location and number of nonzero entries on the main diagonal. [ABSTRACT FROM AUTHOR]

Published
2015
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182. Trace index of a (0,1)-matrix.

Author

Brualdi, Richard A. and Fritscher, Eliseu

Subjects
*MATRICES (Mathematics), *MATHEMATICAL constants, *NUMBER theory, *SET theory, *INTEGERS
Abstract

For-matrices in general, and for-matrices with a constant numberof 1s in each row and column, we determine the possible sets of traces of such matrices as its rows are permuted. Except for some special matrices, which are identified, the set of such traces is a consecutive set of integers from. [ABSTRACT FROM AUTHOR]

Published
2015
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183. A Generalization of Alternating Sign Matrices.

Author

Brualdi, Richard A. and Kim, Hwa K.

Subjects
*MATRICES (Mathematics), *GENERALIZATION, *ALGORITHM software, *PERMUTATION groups, *STATISTICAL physics
Abstract

In alternating sign matrices, the first and last nonzero entry in each row and column is specified to be +1. Such matrices always exist. We investigate a generalization by specifying independently the sign of the first and last nonzero entry in each row and column to be either a +1 or a −1. We determine necessary and sufficient conditions for such matrices to exist whose proof contains an algorithm for their construction. [ABSTRACT FROM AUTHOR]

Published
2015
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193. Index.

Author

Brualdi, Richard A.

Published
2006

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