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arXiv · 1801.00438

On eigenfunctions and maximal cliques of Paley graphs of square order

Sergey Goryainov·Vladislav V. Kabanov·Leonid Shalaginov·Alexandr Valyuzhenich
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Abstract

In this paper we find new maximal cliques of size $\frac{q+1}{2}$ or $\frac{q+3}{2}$, accordingly as $q\equiv 1(4)$ or $q\equiv 3(4)$, in Paley graphs of order $q^2$, where $q$ is an odd prime power. After that we use new cliques to define a family of eigenfunctions corresponding to both non-principal eigenvalues and having the cardinality of support $q+1$, which is the minimum by the weight-distribution bound.

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Sergey Goryainov, Vladislav V. Kabanov, Leonid Shalaginov, Alexandr Valyuzhenich. 2018-01-01. On eigenfunctions and maximal cliques of Paley graphs of square order. https://doi.org/10.1016/j.ffa.2018.05.001

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