Malaya J. Mat. 3(3)(2015) 312–317 Super Edge-antimagic Graceful labeling of Graphs G. Marimuthu a, * and P. Krishnaveni b a,b Department of Mathematics, The Madura College, Madurai–625011, Tamil Nadu, India. Abstract For a graph G = (V,E), a bijection g from V (G) ∪ E(G) into {1, 2,..., |V (G)| + |E(G)|} is called (a, d)-edge-antimagic graceful labeling of G if the edge-weights w(xy)= |g(x)+ g(y) − g(xy)|, xy ∈ E(G), form an arithmetic progression starting from a and having a common difference d. An (a, d)-edge-antimagic graceful labeling is called super (a, d)-edge-antimagic graceful if g(V (G)) = {1, 2,..., |V (G)|}. Note that the notion of super (a, d)-edge-antimagic graceful graphs is a generalization of the article “G. Marimuthu and M. Balakrishnan, Super edge magic graceful graphs, Inf.Sci.,287( 2014)140–151”, since super (a, 0)-edge-antimagic graceful graph is a super edge magic graceful graph.We study super (a, d)-edge-antimagic graceful properties of certain classes of graphs, including complete graphs and complete bipartite graphs. Keywords: Edge-antimagic graceful labeling, Super edge-antimagic graceful labeling. 2010 MSC: 34G20. c 2012 MJM. All rights reserved. 1 Introduction We consider finite undirected nontrivial graphs without loops and multiple edges. We denote by V (G) and E(G) the set of vertices and the set of edges of a graph G, respectively. Let |V (G)| = p and |E(G)| = q be the number of vertices and the number of edges of G respectively. General references for graph-theoretic notions are [2, 24]. A labeling of a graph is any map that carries some set of graph elements to numbers. Kotzig and Rosa [15, 16] introduced the concept of edge-magic labeling. For more information on edge-magic and super edge- magic labelings, please see [10]. Hartsfield and Ringel [11] introduced the concept of an antimagic labeling and they defined an antimagic labeling of a (p, q) graph G as a bijection f from E(G) to the set {1, 2,...,q} such that the sums of label of the edges incident with each vertex v ∈ V (G) are distinct. (a, d)-edge-antimagic total labeling was introduced by Simanjuntak, Bertault and Miller in [22]. This labeling is the extension of the notions of edge-magic labeling, see [15, 16]. For a graph G =(V,E), a bijection g from V (G) ∪ E(G) into {1, 2,..., |V (G)| + |E(G)|} is called a (a, d)- edge-antimagic total labeling of G if the edge-weights w(xy)= g(x)+ g(y)+ g(xy), xy ∈ E(G), form an arithmetic progression starting from a and having a common difference d. The (a, 0)-edge-antimagic total labelings are usually called edge-magic in the literature (see [8, 9, 15, 16]). An (a, d)-edge antimagic total labeling is called super if the smallest possible labels appear on the vertices. All cycles and paths have a (a, d)-edge antimagic total labeling for some values of a and d, see [22]. In [1], Baca et al. proved the (a, d)-edge-antimagic properties of certain classes of graphs. Ivanco and Luckanicova [13] described some constructions of super edge-magic total (super (a, 0)-edge-antimagic total) labelings for * Corresponding author. E-mail address: yellowmuthu@yahoo.com (G. Marimuthu), krishnaswetha82@gmail.com(P. Krishnaveni).