Subdivisions of Contra Harmonic Mean Graphs

Abstract

A graph $G(V, E)$ is called a Contra Harmonic mean graph with p vertices and q edges, if it is possible to label the vertices $x\in V$ with distinct elements $f(x)$ from $0, 1,\dots, q$ in such a way that when each edge $e=uv$ is labeled with $f(e=uv)=$$\left\lceil \frac{f(u)^{2} +f(v)^{2} }{f(u)+f(v)} \right\rceil $ or $\left\lfloor \frac{f(u)^{2} +f(v)^{2} }{f(u)+f(v)} \right\rfloor $ with distinct edge labels. The mapping $f$ is called Contra Harmonic mean labeling of G.