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New Results on Vertex Prime Graphs

Dr. A. Selvam Avadayappan, R. Sinthu

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.