Super Lehmer-3 Mean Labeling of Tree Related Graphs

Abstract

Let $f:V(G)\to \left\{1,2,\dots,p+q\right\}$ be an injective function .The induced edge labeling $f^{*} (e=uv)$ is defined by $f^{*} (e)=\left\lceil \frac{f(u)^{3} +f(v)^{3} }{f(u)^{2} +f(v)^{2} } \right\rceil$ (or) $\left\lfloor \frac{f(u)^{3} +f(v)^{3} }{f(u)^{2} +f(v)^{2} } \right\rfloor $, then \textit{f} is called Super Lehmer-3 mean labeling, if $\left\{f(V(G))\right\}U\left\{f(e)/e\in E(G)\right\}=\left\{1,2,3,\dots,p+q\right\}$. A graph which admits Super Lehmer-3 Mean labeling is called Super Lehmer-3 Mean graph. In this paper we prove that $P_{m} \Theta K_{1,n} $, $(P_{m} ,S_{n} )$.