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A handicap distance antimagic labeling of a graph G=(V,E) with n vertices is a bijection f:Vβ{1,2,β¦,n} with the property that f(xiβ)=i and the sequence of the weights w(x1β),w(x2β),β¦,w(xnβ) (where w(xiβ)=xjββN(xiβ)ββf(xjβ)) 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. We construct (nβ7)-regular handicap distance antimagic graphs for every order nβ‘2(mod4) 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 nβ7
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