A Graph G = (V,E) with p vertices and q edges is said to be a Geometric mean graph if it is possible to label the vertices xV with distinct labels f(x) from 1,2…..q+1 in such a way that when each edge e=uv is labeled with f(e=uv) = (or) , then the resulting edge labels are all distinct. In this case, f is called Geometric mean labeling of G. In this paper we prove that,

A Graph G=(V,E) with p vertices and q edges is said to be a Geometric mean if it is possible to label the vertices xv with distinct labels f(x) from 1,2,….q+1 in such a way that when each edge e=uv is labeled with f(e=uv) = ⌈√ () ()⌉ or ⌊√ () () ⌋, then the resulting edge labels are distinct. In this case f is called Geometric mean labeling of G. In this paper we investigate the Geometric mean labeling behavior for some new families of Graphs.

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