"Radio Harmonic Mean Number of Complete Graphs"

Authors

Dr. K. Amuthavalli
Government Arts and Science College, Veppanthattai, Perambalur,Tamilnadu, Affiliated to Bharathidasan University

R. Revathy
Shri S.S.Shasun Jain College for Women, T.Nagar, Chennai, Tamilnadu, India.

Abstract

A radio harmonic mean labeling of a connected graph G is a one to one map f from the vertex set V(G) to the set of natural numbers N such that for two distinct vertices u and v of G, ( , ) 1 ( ) 2 ( ) ( ) ( ) ( ) f u f v d u v diam G f u f v   + ≥ +     + .The radio harmonic mean number of f, rhmn(f) is the maximum number assigned to any vertex of G. The radio harmonic mean number of G, rhmn(G) is the minimum value of rhmn( f ) taken over all radio harmonic mean labeling f of G. In this paper we have determined the radio harmonic mean number of complete graph , complete bipartite graph and complete tripartite graph. AMS Subject classification : 05C78