Abstract
We give a theoretical proof of the fact that the orthomorphism graph of group \(\mathbb{Z}_2 \times \mathbb{Z}_4\) has maximal clique 2 by determining the structure of the graph.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
L. Q. Chang and S. S. Tai, On the orthogonal relations among orthomorphisms of noncommutative groups of small orders, Acta Math. Sinica 14 (1964), 471–480 (in Chinese); translated in Chinese Math. Acta, 5 (1964), 506–515.
A. B. Evans, Orthomorphism Graphs of Groups , Lecture Notes in Math., vol. 1535, Springer-Verlag (Berlin, 1992).
A. B. Evans, Orthogonal Latin Squares Based on Groups, Springer (Cham, 2018).
A. B. Evans, Orthogonal Latin square graphs based on groups of order 8, Austral. J. Comb., 80 (2021), 116–142.
D. M. Johnson, A. L. Dulmage and N. S. Mendelsohn, Orthomorphisms of groups and orthogonal latin squares. I, Canad. J. Math., 13 (1961), 356–372.
D. Jungnickel and G. Grams, Maximal difference matrices of order ≤ 10, Discrete Math., 58 (1986), 199–203.
Acknowledgement
We are grateful to the referees for their insightful comments on the paper.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Jain, V., Pradhan, R. The structure of the orthomorphism graph of \(\mathbb{Z}_2 \times \mathbb{Z}_4\). Acta Math. Hungar. 170, 670–680 (2023). https://doi.org/10.1007/s10474-023-01366-y
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-023-01366-y