Opuscula Math. 37, no. 4 (2017), 557-566
http://dx.doi.org/10.7494/OpMath.2017.37.4.557
Opuscula Mathematica
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.
Mathematics Subject Classification: 05C78.
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- Dalibor Froncek
- University of Minnesota, Duluth, Department of Mathematics and Statistics, 1117 University Dr., Duluth, MN 55812, U.S.A.
- Communicated by Gyula O.H. Katona.
- Received: 2016-09-07.
- Revised: 2017-01-30.
- Accepted: 2017-01-31.
- Published online: 2017-04-28.
