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Quotient-Complete Arc-Transitive Latin Square Graphs from Groups

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Abstract

We consider latin square graphs \(\varGamma = \text {LSG}(H)\) of the Cayley table of a given finite group H. We characterize all pairs \((\varGamma ,G)\), where G is a subgroup of autoparatopisms of the Cayley table of H such that G acts arc-transitively on \(\varGamma \) and all nontrivial G-normal quotient graphs of \(\varGamma \) are complete. We show that H must be elementary abelian and determine the number k of complete normal quotients. This yields new infinite families of diameter two arc-transitive graphs with \(k = 1\) or \(k = 2\).

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Acknowledgements

The author thanks Pablo Spiga for introducing the graphs and corresponding automorphism groups in Example 3 and John Bamberg for pointing out the connection to finite nets.

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Authors and Affiliations

  1. Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines

    Carmen Amarra

  2. Natural Sciences Research Institute, College of Science, University of the Philippines Diliman, Quezon City, Philippines

    Carmen Amarra

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  1. Carmen Amarra
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Correspondence to Carmen Amarra.

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Amarra, C. Quotient-Complete Arc-Transitive Latin Square Graphs from Groups. Graphs and Combinatorics 34, 1651–1669 (2018). https://doi.org/10.1007/s00373-018-1948-y

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  • DOI: https://doi.org/10.1007/s00373-018-1948-y

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