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We consider the Cayley graph on the additive group of \(\mathbb {F}_{q^3}\) , with \(q=2^m\) , whose connection set is the norm-one torus. We show that the number of common neighbours of two distinct vertices depends only on the norm of their difference. For the norm-one class we obtain an explicit codegree formula and, as a consequence, an exact triangle count.

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Codegrees and an Exact Triangle Formula for the Norm-One Cayley Graph over  \(\mathbb {F}_{q^3}\) in Characteristic 2

  • 会议论文

  • 发表日期：

    2026年

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  • Francisco-Javier Soto

摘要

We consider the Cayley graph on the additive group of \(\mathbb {F}_{q^3}\) , with \(q=2^m\) , whose connection set is the norm-one torus. We show that the number of common neighbours of two distinct vertices depends only on the norm of their difference. For the norm-one class we obtain an explicit codegree formula and, as a consequence, an exact triangle count.