Antimagic Labeling of Some Biregular Bipartite Graphs

An antimagic labeling of a graph G = (V, E) is a one-to-one mapping from E to {1, 2, . . ., |E|} such that distinct vertices receive different label sums from the edges incident to them. G is called antimagic if it admits an antimagic labeling. It was conjectured that every connected graph other than K-2 is antimagic. The conjecture remains open though it was verified for several classes of graphs such as regular graphs. A bipartite graph is called (k, k ')-biregular, if each vertex of one of its parts has the degree k, while each vertex of the other parts has the degree k '. This paper shows the following results. (1) Each connected (2, k)-biregular (k >= 3) bipartite graph is antimagic; (2) Each (k, pk)-biregular (k >= 3, p >= 2) bipartite graph is antimagic; (3) Each (k, k(2) + y)-biregular (k >= 3, y >= 1) bipartite graph is antimagic.