@article{article_259727, title={Regular handicap tournaments of high degree}, journal={Journal of Algebra Combinatorics Discrete Structures and Applications}, volume={3}, pages={159–164}, year={2016}, DOI={10.13069/jacodesmath.22530}, author={Froncek, Dalibor and Shepanik, Aaron}, abstract={<p>A  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 the weights $w(x_1),w(x_2),\ldots,w(x_n)$ <br /> (where $w(x_i)=\sum\limits_{x_j\in N(x_i)}f(x_j)$) <br /> forms an increasing arithmetic progression with difference one. A graph $G$ is a {\em handicap distance antimagic graph} if it allows a handicap distance antimagic labeling. <br /> We construct $(n-7)$-regular handicap distance antimagic graphs for every order $n\equiv2\pmod4$ 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 $n-7$. </p>}, number={3}, publisher={iPeak Academy}