1Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli-627 012, Email: somumsu@rediffmail.com
2Department of Mathematics, KG College of Arts and Science, Coimbatore -641 035, Email: vidhyaranLp@kgcas.com
3Department of Mathematics, Sri Paramakalyani College, Alwarkurichi -627412, Email: ponrajmath@gmail.com
Online published on 22 February, 2013.
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 Pn, cycle Cn, a complete graph Kn, n ≤4, comb, ladder and some more special graphs are Geometric mean graphs. Also we prove that Kn, n >4 and complete bipartite graph K1,n for n >5 are not geometric mean graphs.
Graph, Geometric mean graph, Path, Cycle, Comb, Ladder
