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Antimagic labeling of the union of two stars

Abstract:

Let G be a graph of order p and size q. An (a, d)-edge-antimagic total labeling of G is a one-to-one map f taking the vertices and edges onto 1,2,...,p + q so that the edge-weights w(u,v) = f(u) + f(v) + f(uv), uv ∈ E(G), form an arithmetic progression, starting from a and having common difference d. Moreover, such a labeling is called super (a, d)edge-antimagic total if f(V(G)) = {1,2,...,p}. This paper considers such labelings applied to a disjoint union of two stars K1,m and K1,n.