Abstract:
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 2, the greatest common divisor of the labels on its incident edges is 1. A graph that admits a vertex prime labeling is called a vertex prime graph.
In this paper, we prove that mK3,3 and mK4,4 are vertex prime graphs, where m is any positive integer.
Keywords: Labeling of graphs, vertex prime labeling of graphs.