5 research outputs found
Regular handicap tournaments of high degree
A handicap distance antimagic labeling of a graph with vertices is a bijection with the property that and the sequence of the weights (where ) forms an increasing arithmetic progression with difference one. A graph is a {\em handicap distance antimagic graph} if it allows a handicap distance antimagic labeling. We construct -regular handicap distance antimagic graphs for every order with a few small exceptions. This result complements results by Kov\'a\v{r}, Kov\'a\v{r}ov\'a, and Krajc~[P. Kov\'a\v{r}, T. Kov\'a\v{r}ov\'a, B. Krajc, On handicap labeling of regular graphs, manuscript, personal communication, 2016] who found such graphs with regularities smaller than
Graph Labelings and Tournament Scheduling
University of Minnesota M.S. thesis. May 2015. Major: Applied and Computational Mathematics. Advisor: Dalibor Froncek. 1 computer file (PDF); viii, 55 pages.During my research I studied and became familiar with distance magic and distance antimagic labelings and their relation to tournament scheduling. Roughly speaking, the relation is as follows. Let the vertices on the graph represent teams in a tournament, and let an edge between two vertices a and b represent that team a will play team b in the tournament. Further, suppose we can rank the teams based on previous games, say, the preceding season. These integer rankings become labels for the vertices. Of particular interest were handicap tournaments, that is, tournaments designed to give each team a more balanced chance of winning
Regular handicap tournaments of high degree
A Β handicap distance antimagic labeling of a graph with vertices is a bijection with the property that and the sequence of the weights (where ) forms an increasing arithmetic progression with difference one. A graph is a {\em handicap distance antimagic graph} if it allows a handicap distance antimagic labeling. We construct -regular handicap distance antimagic graphs for every order with a few small exceptions. This result complements results by Kov\'a\v{r}, Kov\'a\v{r}ov\'a, and Krajc~[P. Kov\'a\v{r}, T. Kov\'a\v{r}ov\'a, B. Krajc, On handicap labeling of regular graphs, manuscript, personal communication, 2016] who found such graphs with regularities smaller than .</p
On regular handicap graphs of order mod 8
A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection fΜ : V β {1, 2, β¦, n} with the property that fΜ(xi) = i, the weight w(xi) is the sum of labels of all neighbors of xi, and the sequence of the weights w(x1), w(x2), β¦, w(xn) forms an increasing arithmetic progression. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct r-regular handicap distance antimagic graphs of order for all feasible values of r.</p