On Super Edge-Antimagicness of Circulant Graphs

A labeling of a graph is a mapping that carries some sets of graph elements into numbers (usually the positive integers). An $$(a,d)$$(a,d)-edge-antimagic total labeling of a graph $$G(V,E)$$G(V,E) is a one-to-one mapping $$f$$f from $$V(G)\cup E(G)$$V(G)∪E(G) onto the set $$\{1,2,\dots , |V(G)|+|E(G)|\}$${1,2,⋯,|V(G)|+|E(G)|}, such that the set of all the edge-weights, $$wt_f (uv) = f(u) +f(uv)+f(v)$$wtf(uv)=f(u)+f(uv)+f(v), $$uv\in E(G)$$uv∈E(G), forms an arithmetic sequence starting from $$a$$a and having a common difference $$d$$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.