Abstract
For a graph G = (V, E) with p vertices and q edges, a bijection f from V (G) boolean OR E(G) onto {1, 2, ... ,p + q} is called an (a, d)-edge-antimagic total labeling of G if the edge-weights {w(uv) : w(uv) = f (u) + f(v) + f(uv), uv epsilon E(G)}, form an arithmetic progression starting from a and having common difference d. We study graphs with no edge-antimagic labeling and show how to construct labelings for cycles with d = 3. We also show the relationship between the sequential graphs and the graphs having an (a, d)-edge-antimagic vertex labeling.