Harmonic Mean Labelling of Subdivision and Related Graphs

Abstract

A graph G=(V,E) with p vertices and q edges is said to be a mean graph if it is possible to label the vertices with distinct elements f(x) from 0,1,2,…..q in such a way that when each edge is labelled with if is even and if is odd, then the resulting edge labels are distinct. is called a mean labelling of G. In this paper, we investigate the mean labelling of caterpillar, dragon, arbitrary super subdivision of a path and some graphs which are obtained from cycles and stars.