Some results on Grotzsch graph

In this paper, we show that the Grotzsch graph Gz has admits Vertex Prime Labeling. When the graph has Vertex Prime Labeling that graph is called Vertex Prime graph. A Graph G = (V, E) is said to have a Vertex Prime Labeling if its edges can be labeled with distinct integers from {1,2,3,⋯, |E|} such that for each vertex of degree at least two, the Greatest Common Divisor of the labels on its incident edges is 1. We also prove that Vertex Prime Labeling in the context of the operation of duplication.