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On Super Edge-Antimagicness of Circulant Graphs

Abstract:

A labeling of a graph is a mapping that carries some sets of graph elements into numbers (usually the positive integers). An (a,d)-edge-antimagic total labeling of a graph G(V,E) is a one-to-one mapping f from V(G)∪E(G) onto the set {1,2,⋯,|V(G)|+|E(G)|}, such that the set of all the edge-weights, wtf(uv)=f(u)+f(uv)+f(v), uv∈E(G), forms an arithmetic sequence starting from a and having a common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper we study the existence of such labelings for circulant graphs.