TY  - JOUR
ID  - Froncek2017
LB  - Froncek2017
AU  - Froncek, Dalibor
TI  - A note on incomplete regular tournaments with handicap two of order n≡8(mod 16)
ST  - A note on incomplete regular tournaments with handicap two of order n≡8(mod 16)
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 4
SP  - 557
EP  - 566
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.4.557
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.4.557
AB  - 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 \(6\leq k\leq n-50\).
KW  - incomplete tournaments
KW  - handicap tournaments
KW  - distance magic labeling
KW  - handicap labeling
SN  - 1232-9274
ER  -