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THIRD-REGULAR BI-EMBEDDINGS OF LATIN SQUARES

Published online by Cambridge University Press:  25 August 2010

D. M. DONOVAN ,
M. J. GRANNELL  and
T. S. GRIGGS
D. M. DONOVAN
Affiliation:
Centre for Discrete Mathematics and Computing, University of Queensland, St Lucia 4072, Australia e-mail: dmd@maths.uq.edu.au
M. J. GRANNELL
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK e-mail: M.J.Grannell@open.ac.uk
T. S. GRIGGS
Affiliation:
Department of Mathematics and Statistics, The Open University, Walton Hall, Milton Keynes MK7 6AA, UK e-mail: t.s.griggs@open.ac.uk
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Abstract

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For each positive integer n ≥ 2, there is a well-known regular orientable Hamiltonian embedding of Kn, n, and this generates a regular face 2-colourable triangular embedding of Kn, n, n. In the case n ≡ 0 (mod 8), and only in this case, there is a second regular orientable Hamiltonian embedding of Kn, n. This paper presents an analysis of the face 2-colourable triangular embedding of Kn, n, n that results from this. The corresponding Latin squares of side n are determined, together with the full automorphism group of the embedding.

Keywords

05B1505C10
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 3 , September 2010 , pp. 497 - 503
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

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