We study the relationship between homogeneous bent functions and some intersection graphs of a special type that are called Nagy graphs and denoted by Γ_(n,k). The graph Γ_(n,k) is the graph whose vertices correspond to (n_k) unordered subsets of size k of the set 1,..., n. Two vertices of Γ(_n,k) are joined by an edge whenever the corresponding k-sets have exactly one common element. Those n and k for which the cliques of size k + 1 are maximal in Γ_(n,k) are identified. We obtain a formula for the number of cliques of size k + 1 in Γ(_n,k) for n = (k + 1)k/2. We prove that homogeneous Boolean functions of 10 and 28 variables obtained by taking the complement to the cliques of maximal size in Γ(₁₀,4) and Γ_(28,7) respectively are not bent functions.

中文翻译：

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齐次弯曲函数与Nagy图之间的关系

我们研究了均匀弯曲函数与某些特殊类型的相交图之间的关系，这些相交图称为Nagy图，并用Γ _{（n，k）表示}。图Γ _（n，k）是其顶点对应于集合1，...，n的大小为k的（n _k）个无序子集的图。每当对应的k个集恰好具有一个公共元素时，Γ（_n，k）的两个顶点就由一条边连接。那些Ñ和ķ为其大小的派系ķ + 1是在最大Γ _（N，K）被识别。对于n =（k + 1）k / 2 _，我们在Γ（_n，k）中获得了大小为k + 1的集团数量的公式。我们证明10个28的变量均相布尔函数通过采取补充最大尺寸的派系中Γ（得到₁₀，4）和Γ _（28,7）分别没有弯曲的功能。