The graph of minimal distances of bent functions and its properties

A notion of the graph of minimal distances of bent functions is introduced. It is an undirected graph (V , E) where V is the set of all bent functions in 2k variables and (f, g) ∈ E if the Hamming distance between f and g is equal to 2 (it is the minimal possible distance between two different bent functions). The maximum degree of the graph is obtained and it is shown that all its vertices of maximum degree are quadratic. It is proven that a subgraph of the graph induced by all functions affinely equivalent to Maiorana—McFarland bent functions is connected.