Regular handicap graphs of order n ≡ 4 (mod 8)

Dalibor Froncek (Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, USA)
Aaron Shepanik (Department of Mathematics and Statistics, University of Minnesota Duluth, Duluth, USA)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications

A handicap distance antimagic labeling of a graph G = (V, E) with n vertices is a bijection f : V → {1, 2, …, n} with the property that f(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),…,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 n ≡ 4 (mod 8) for all feasible values of r.