Construction of Super Edge Magic Total Graphs K. A. Sugeng(1,2) and W. Xie(1) (l)School of Information Technology and Mathematical Sciences, University of Ballarat, VIC 3353, Australia. e-mail:{k.sugeng.w.xie}@ballarat.edu.au (2)Department of Mathematics, University ofIndonesia, Depok 16424, Indonesia. Abstract In this paper, we investigate the adjacency matrix of (a, d)-edge antimagic vertex graph and use this graph to construct other super edge magic total graphs with the same edge- weight set. Additionally, by combining known super edge magic total labeled graphs, we give a construction for a new super edge magic total graph. Keywords: adjacency matrix, edge antimagic vertex labeling, super edge magic labeling. 1 Introduction Let G be a finite simple undirected graph. The set of vertices and edges of a graph G will be denoted by V(G) and E(G), respectively, v = IV(G) I and e = IE(G)I. For simplicity, we denote V(G) by V and E(G) by E. A labeling of a graph G is a mapping that carries a set of graph elements into a set of numbers (usually positive integers), called labels. Kotzig and Rosa in 1970 introduced edge magic total labeling [5]. An (a, d)-edge antimagic vertex (EAV) labeling is a one-to-one mapping f from V onto the in- tegers 1,2, ... ,v with the property that for every xy E E, the edge-weight set {f(x) + f(y)lx, y E V}={ a, a + d, a + 2d, ... , a + (e - 1 )d} for some positive integers a and d. A graph that has an (a, d)-edge antimagic vertex labeling is called an (a, d)- edge antimagic vertex graph. Since in this paper, we only consider the case of d = 1, then for simplicity we denote (a,l)-EAV graph as EAV graph. An edge magic total (EMT) labeling is a one-to-one mapping f from VuE onto the integers 1,2, ... ,v·+ e with the property that for every (x, y) in E, f(x) + f(y) + f(xy) = k for some constant k. A graph that has an edge magic total labeling is called an edge magic total graph. An edge magic total labeling is called a super edge magic total (SEMI) labeling if f(V) = {I, 2, ... , v} and a graph that has SEMT labeling is called a SEMT graph.