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Every 4-Equivalenced Association Scheme is Frobenius

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Abstract

For a positive integer k, we say that an association scheme \((\varOmega ,S)\) is k-equivalenced if each non-diagonal element of S has valency k. An association scheme \((\varOmega ,S)\) is called Frobenius when the set S is equal to the set of orbitals of a Frobenius group G on a finite set \(\varOmega \). It is known that every k-equivalenced association scheme is Frobenius when k=2, 3. In this paper, we show that every 4-equivalenced association scheme is Frobenius, and give some properties of a 4-equivalenced association scheme.

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Acknowledgements

The author would like to express deepest gratitude to the anonymous referees for their careful reading and valuable comments.

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  1. Department of Mathematics, Postech, 77 Cheongam-ro, Nam-gu, Pohang, Gyeongbuk, South Korea

    Bora Moon

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  1. Bora Moon
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Correspondence to Bora Moon.

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Moon, B. Every 4-Equivalenced Association Scheme is Frobenius. Graphs and Combinatorics 36, 401–414 (2020). https://doi.org/10.1007/s00373-019-02037-y

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  • DOI: https://doi.org/10.1007/s00373-019-02037-y

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