Super Mean Labeling of Some Subdivision Graphs

R. Vasuki, P. Sugirtha, J. Venkateswari

Let $G$ be a graph and $f:V(G)\rightarrow\{1,2,3,�,p+q\}$ be an injection. For each edge $e=uv$, the induced edge labeling $f^*$ is defined as follows: \[f^*(e)=\begin{cases} \frac{f(u)+f(v)}{2},&\quadext{if $f(u)+f(v)$ is even,} \frac{f(u)+f(v)+1}{2},&\quadext{if $f(u)+f(v)$ is odd.} \end{cases} \] Then $f$ is called super mean labeling if $f(V(G))\cup \{f^*(e):e\in E(G)\}=\linebreak\{1,2,3,�, p+q\}$. A graph that admits a super mean labeling is called super mean graph. In this paper, we have studied the super meanness property of the subdivision of the $H$-graph $H_n$, $H_n\odot K_1, H_n\odot S_2$, slanting ladder, $T_n\odot K_1, C_n\odot K_1$ and $C_n@\,C_m$.