Edge-magic total labelings on connected and disconnected graphs

Abstract

An edge-magic total labeling on a graph G with the vertex-set V(G) and the edge-setE(G) is a one-to-one function f from V(G) U E(G) onto the set { 1, 2,..., p + q } where p = (G) and q = (G) with the property that, for any edge xy, f(x) + f(xy) + f(y) = k for some constant k. This thesis surveys and collects many classes of graphs that can admit an edge-magic total labeling. Moreover, we prove that the following graphs have edge-magic total labelings: an (n,1)-kite when n is odd for some different values of k, an (n,m)-pineapple when n is odd, the graph m(n,1)-kite: the disjoint union of m copies of (n,1)-kite, when m and n are odd and the graph mPnUmK1: the graph consists of the disjoint union of m copies of Pn and the disjoint union of m copies of K1, when m is odd and n is even.