Sum Labeling for Some Star and Cycle Related Special Graphs

A sum labeling is a mapping from the vertices of G into the positive integers such that, for any two vertices u, v V (G) with labels (u) and (v), respectively, (uv) is an edge iff (u) + (v) is the label of another vertex in V (G). Any graph supporting such a labeling is called a sum graph. It is necessary to add (as a disjoint union) a component to sum label a graph. This disconnected component is a set of isolated vertices known as isolates and the labeling scheme that requires the fewest isolates is termed optimal. The number of isolates required for a graph to support a sum labeling is known as the sum number of the graph. In this paper, we will obtain optimal sum labeling scheme for some star and cycle related special graphs.