Abstract
In this paper, we investigate the existence of idempotent Latin squares for which each conjugate is orthogonal to precisely its own transpose. We show that the spectrum of Latin squares with this desired property contains all integers v⩾8, with the possible exception of 10 and 11. As an application of our results, it is shown that for all integers v⩾8, with the possible exception of 10 and 11, there exists an idempotent Latin square of order v that realizes the one-regular graph on 6 vertices as a conjugate orthogonal Latin square graph.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
