Edge-antimagic graphs

For a graph G = (V ,E), a bijection g from V (G) ∪ E(G) into {1, 2, . . . , |V (G)| + |E(G)|} is called (a, d)-edge-antimagic total labeling of G if the edge-weights w(xy) = g(x) + g(y) + g(xy), xy belong to E(G), form an arithmetic progression starting from a and having common difference d. An (a, d)-edge-antimagic total labeling is called super (a, d)-edge-antimagic total if g(V (G)) = {1, 2, . . . , |V (G)|}. We study super (a, d)-edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs