On Prime Labeling of some Classes of Graphs

Abstract

Graph labeling is an important area of research in Graph theory. There are many kinds of graph labeling such as Graceful labeling, Magic labeling, Prime labeling, and other different labeling techniques.In this paper the Prime labeling of certain classes of graphs are discussed.It is of interest to note that H-graph which is a 3 –regular graph satisfy Prime labeling. A Gear graph is a graph obtained from Wheel graph, with a vertex added between each pair of adjacent vertices of an outer cycle. It is proved in general this graph is Prime. Yet another class of graphs is the Sun flower graph and corona of Cycle graph Cn and K1,3 .A stepwise algorithm is given to prove that both these classes of graphs satisfy Prime labeling.