Quadrangularity and Strong Quadrangularity in Tournaments.
Australasian Journal of Combinatorics
The pattern of a matrix M is a (0,1)-matrix which replaces all non-zero entries of M with a 1. A directed graph is said to support M if its adjacency matrix is the pattern of M. If M is an orthogonal matrix, then a digraph which supports M must satisfy a condition known as quadrangularity. We look at quadrangularity in tournaments and determine for which orders quadrangular tournaments exist. We also look at a more restrictive necessary condition for a digraph to support an orthogonal matrix, and give a construction for tournaments which meet this condition.
|Title:||Quadrangularity and Strong Quadrangularity in Tournaments|
|Additional information:||12 pages|
|Keywords:||math.CO, math.CO, quant-ph, 05C20; 05C50; 05C75|
|UCL classification:||UCL > School of BEAMS
UCL > School of BEAMS > Faculty of Engineering Science
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