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HADAMARD MATRICES AND 1-FACTORIZATIONS OF COMPLETE GRAPHS

Part of: Designs and configurations Graph theory Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  11 February 2019

Keith Ball ,
Oscar Ortega-Moreno  and
Maria Prodromou
Keith Ball
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, U.K. email kmb120205@googlemail.com
Oscar Ortega-Moreno
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, U.K. email o.a.ortega-moreno@warwick.ac.uk
Maria Prodromou
Affiliation:
Mathematics Department, Westminster Academy, The Naim Dangoor Centre, 255 Harrow Road, London W2 5EZ, U.K. email m.n.prodromou@gmail.com
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Abstract

We discuss 1-factorizations of complete graphs that “match” a given Hadamard matrix. We prove the existence of these factorizations for two families of Hadamard matrices: Walsh matrices and certain Paley matrices.

MSC classification

Primary: 05B20: Matrices (incidence, Hadamard, etc.) 05C70: Factorization, matching, partitioning, covering and packing 11T99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 65 , Issue 3 , 2019 , pp. 488 - 499
Copyright
Copyright © University College London 2019 

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Footnotes

Oscar Ortega-Moreno was supported by the Mexican National Council of Science and Technology (CONACYT) grant #579817.

References

Moree, P., On primes in arithmetic progression having a prescribed primitive root. J. Number Theory 78(1) 1999, 85–98.Google Scholar
Paley, R. E., On orthogonal matrices. Stud. Appl. Math. 12(1–4) 1933, 311–320.Google Scholar