Geometric mean labeling of graphs

In this paper we introduce a new labeling called Geometric mean labeling. 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 XEV with distinct labels f(x) from 1,2 ….q+1 in such a way that when each edge e = uv is labeled with (or) then the edge labels are distinct.

Here we prove that the path P_n, cycle C_n, a complete graph K_n, n ≤4, comb, ladder and some more special graphs are Geometric mean graphs. Also we prove that K_n, n >4 and complete bipartite graph K_1,n for n >5 are not geometric mean graphs.