Edge-antimagic graphs

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