Weighted antimagic labeling

In this work, we prove that all the complete bipartite graphs Kp,q, are weighted-0-antimagic when 2≤p≤q and q≥3. Moreover, an algorithm is proposed that computes in polynomial time a (w,0)-antimagic labeling of the graph. Our result implies that if H is a complete partite graph, with H≠K1,q, K2,2, then any connected graph G containing H as a spanning subgraph is antimagic.