1Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli, (Tamilnadu)-627 012. Email: somumsu@rediffmail.com
2Department of Mathematics, Sree Ayyappa College for Women, Chunkankadai -629 807, Kanyakumart district, Tamilnadu Email: sssandhya2009@gmail.com
Online published on 22 February, 2013.
In this paper we introduce a new type of labeling called skolem harmonic mean labeling. A (p, q) graph G is a skolem harmonic mean graph if it is possible to label the vertices XEV with distinct labels f(x) from 1, 2, …, P in such a way that when each edge e=uv is labeled with (or) then the resulting edges get distinct labels from 1,2 ….p. In this case f is called a skolem harmonic mean labeling. We prove that the path Pn, cycle Cn, complete graph Kn, n ≤ 3, comb, crown and some more special of skolem harmonic mean graphs. We also prove that the complete bipartite graph. K1,n, n > 11 is not a skolem harmonic mean graphs.
Graph, Harmonic mean graph, Skolem harmonic mean graph, Path, Cycle, Complete graph, Complete bipartite graph, Comb, Crown
