A note on incomplete regular tournaments with handicap two of order n≡8(mod 16)

Abstract

A \(d\)-handicap distance antimagic labeling of a graph \(G=(V,E)\) with \(n\) vertices is a bijection \(f:V\to \{1,2,\ldots ,n\}\) with the property that \(f(x_i)=i\) and the sequence of weights \(w(x_1),w(x_2),\ldots,w(x_n)\) (where \(w(x_i)=\sum_{x_i x_j\in E}f(x_j)\)) forms an increasing arithmetic progression with common difference \(d\). A graph \(G\) is a \(d\)-handicap distance antimagic graph if it allows a \(d\)-handicap distance antimagic labeling. We construct a class of \(k\)-regular \(2\)-handicap distance antimagic graphs for every order \(n\equiv8\pmod{16}\), \(n\geq56\) and \(6\leq k\leq n-50\).

Keywords

• incomplete tournaments
• handicap tournaments
• distance magic labeling
• handicap labeling