VERTEX PRIME LABELLING ON PLANAR GRAPHS AND CYCLE RELATED GRAPHS.

摘要

A graph with vertex set V is said to be have a vertex prime labeling if its edges are labeled with distinct integers 1,2,3,.......,|E| such that for each vertex of degree at least 2 the greatest common divisor of the labels on its incident edges is 1. A graph which admits prime labeling is called prime graph. In this paper, we shall prove that planar graph Pl_n and Pl_(m,n); parachute graphs, olive trees, special butterfly graph and spl(B_(n,n)) are prime graphs.