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On antimagic labelings of disjoint union of complete s-partite graphs

Abstract:

By an (a, d)-edge-antimagic total labeling of a graph G(V, E) we mean a bijective function f from V(G) U E(G) onto the set {1, 2, ..., V (G) + E (G) } such that tile set of all tile edge-weights, w(uv) = f (u) + f (uv) + f (v), uv ̇E(G), is {α, α + d, α + 2d,..., α+ ( E(G) - 1)d}, for two integers α > 0 and d > 0. In this paper we stu:dy the edge-antimagic properties for tile disjoint union of complete s-partite graphs.