Contra Harmonic Mean Labelling of Graphs

Abstract

A graph labelling is an assignment of integers to the vertices or edges or both subject to certain conditions. A Graph G(V, E) with p vertices and q edges is called a Contra Harmonic mean graph if it is possible to label all the vertices x ∈ V with distinct labels f(x) from {1, 2, 3, 4, …., p } in such a way that each edge e = uv is labelled with

f uv = f(u) 2 + f(v) 2

f u +f(v)

or f uv = f(u) 2 + f(v) 2

f u +f(v)

are distinct.