No abstract

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 thatf (x i ) = i, the weight w(x i ) is the sum of labels of all neighbors of x i , and the sequence of the weights w(x 1 ), w(x 2 ), . . . , w(x n ) 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 ≡ 0 (mod 8) for all feasible values of r.

No abstract

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 and the sequence of the weights w(x1), w(x2),. .. , w(xn) (where w(xi) = x j ∈N (x i) f (xj)) forms an increasing arithmetic progression with difference one. A graph G is a handicap distance antimagic graph if it allows a handicap distance antimagic labeling. We construct (n − 7)-regular handicap distance antimagic graphs for every order n ≡ 2 (mod 4) with a few small exceptions. This result complements results by Kovář, Kovářová, and Krajc [P. Kovář, T. Kovářová, B. Krajc, On handicap labeling of regular graphs, manuscript, personal communication, 2016] who found such graphs with regularities smaller than n − 7.