A labeling (or valuation) of a graph is a map that carries the graph elements to numbers (usually to the positive integers). The domain will usually be the set of all vertices and edges; such labelings are called total labelings. In the case when all vertices receive smallest labels, then edge-magic total (vertex-magic total) labeling is called super edge- magic total labeling (super vertex-magic total labeling). Some labelings use the vertex set or the edge set alone and they will be referred as vertex- labeling and edge-labeling respectively. Other domains are also possible. There are many types of labelings for example harmonious, cordial, graceful and antimagic. This book studies about the construction of a super edge-magic total la-beling of banana tree as well as for disjoint union of k identical copies of banana trees. We also construct the antimagic total labelings of Harary graphs

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