LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Relationship Between Homogeneous Bent Functions and Nagy Graphs

Photo by johnfo from unsplash

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… Click to show full abstract

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 (nk) 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.

Keywords: homogeneous bent; nagy graphs; bent functions; relationship homogeneous

Journal Title: Journal of Applied and Industrial Mathematics
Year Published: 2019

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.