RELATIONSHIP BETWEEN HOMOGENEOUS BENT FUNCTIONS AND NAGY GRAPHS
We study the relationship between homogeneous bent functions and some intersection graphs of a special type that are called Nagy graphs and denoted by r<sub>(n</sub>,<sub>fc)</sub>. The graph r<sub>(n</sub>,<sub>fc)</sub> is the graph whose vertices correspond to (™) unordered subsets of size к of the set {1,..., n}. Two vertices of r<sub>(</sub>„<sub>jfc)</sub> are joined by an edge whenever the corresponding fc-sets have exactly one common element. Those n and к for which the cliques of size к + 1 are maximal in r<sub>(</sub>„<sub>jfc)</sub> are identified. We obtain a formula for the number of cliques of size к + 1 in r<sub>(</sub>„<sub>jfc)</sub> for n = (k + l)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 Г<sub>(10</sub>,<sub>4</sub>) and r<sub>(28j7)</sub> respectively are not bent functions. Tab. 3, illustr. 2, bibliogr. 9.