Quadrangularity in Tournaments

The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be orthogonal is a property known as combinatorial orthogonality. If...

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Bibliographic Details
Published in:arXiv.org 2004-04
Main Authors: Lundgren, J Richard, Severini, Simone, Stewart, Dustin J
Format: Article
Language:English
Subjects:
Combinatorial analysis
Graph theory
Orthogonality
Online Access:Get full text
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Summary:The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. There are several contexts in which studying the patterns of orthogonal matrices can be useful. One necessary condition for a matrix to be orthogonal is a property known as combinatorial orthogonality. If the adjacency matrix of a directed graph forms a pattern of a combinatorially orthogonal matrix, we say the digraph is quadrangular. We look at the quadrangular property in tournaments and regular tournaments.
ISSN:2331-8422