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)

Dalibor Froncek

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.
• Revised: 2017-01-30.
• Accepted: 2017-01-31.
• Published online: 2017-04-28.