• FURTHER RESULTS ON HARMONIC MEAN GRAPHS

Abstract

A Graph G = (V, E) with p vertices and q edges is called a Harmonic 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(uv) = (or) , then the edge labels are distinct. In this case f is called Harmonic Mean Labeling of G. In this paper we prove that mCn, mCn∪Pk, mCn∪Ck, mCn∪PCk, nk3∪Cm, nk3∪PCm, PmP3 are Harmonic mean graphs. Also we prove that the graph obtained by joining two copies of cycle Cn by a path of arbitrary length is a Harmonic mean graph.