On Super Edge-Magic Total Labeling of Graphs

Abstract

A graph is said to be labeled if we assign di erent labels (usually non-negative integers) to the vertices or the edges (or both) of the graph, otherwise it is said to be unlabeled. These labels are used to identify the vertices and edges of a graph. The process of assigning labels to the vertices or edges of the graph is called graph label-ing. A super edge-magic total labeling (SEMT labeling) of a graph G is a bijection f : V (G)[E(G) ! f1; 2; 3; : : : ; p+qg, such that in addition of being an edge-magic total labeling of G, it satis es another property that f : (V (G)) ! f1; 2; 3; : : : ; pg. Also the egde-weights are calculated as: ff(u) + f(v) + f(uv) : xy 2 E(G)g such that all the edge-weights are same.We constructed super edge magic total labeling of some families of acyclic graphs. The super edge-magic total labeling of reexive w-graphs, extended reexive w-graphs, generalized re exive w-graphs, generalized w-tree and generalized comb was carried out and it was found that these graphs admit all the properties of superedge-magic total labeling.