k-Lehmer three mean labeling of some graphs

Abstract

A function $\mathrm{h}$ is called $\mathrm{k}$ - Lehmer-3 mean graph $\mathrm{G}$ with $\mathrm{r}$ vertices and $\mathrm{s}$ edges, if it is possible to label the vertices $v \in V$ with distinct labels $h(x)$ from $k, k+1, k+2, \ldots, k+s$ in such a way that each edge $e=x y$ is labeled with $h(e)=\left\lceil\frac{h(x)^3+h(y)^3}{h(x)^2+h(y)^2}\right\rceil$ (or) $\left\lfloor\frac{h(x)^3+h(y)^3}{h(x)^2+h(y)^2} \mid\right.$ then the edge labels are distinct.In this paper we proved k-Lehmer-three mean labeling of some standard graphs.