Super Lehmer-3 mean labeling of snake related graphs

Abstract

Let $h:V(G)\to\{1,2,\ldots,p+q\}$ be an injective function. The induced edge labeling $h^* (e=uv)$ is defined by $h^*(e)=\lceil\frac{h(u)^3+h(v)^3}{h(u)^2+h(v)^2}\rceil$ or $\lfloor\frac{h(u)^3+h(v)^3}{h(u)^2+h(v)^2}\rfloor$, then $h$ is called super lehmer - 3 mean labeling, if $\{h(V(G))\}\cup\{h(e)/e\in E(G)\}=\{1,2,\ldots,p+q\}$. A graph which admits Super lehmer - 3 mean labeling is called Super Lehmer - 3 Mean graph. In this paper, we prove that snake related graphs such as Triangular snake $T_\tau$, $T_\tau\odot\underline{K_1}$, $T_\tau\odot\underline{K_2}$, $T_\tau\odot\underline{K_3}$, $T_\tau\odot K_2$, path union of two cycles with corona product $\underline{K_2}$, path union of two cycles admit a path $P_k$ with corona product $\underline{K_2}$, Quadrilateral snake $Q_\tau$, $Q_\tau\odot\underline{K_1}$, $Q_\tau\odot\underline{K_2}$, $Q_\tau\odot\underline{K_3}$ and $Q_\tau\odot K_2$ are all super lehmer - 3 mean graphs.