Geodesic
Super Mean Labeling of Some Subdivision Graphs
Kragujevac Journal of Mathematics, Tome 41 (2017) no. 2, p. 179

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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 $C_n@\,C_m$.
Classification : 05C78
Keywords: Super mean graph, super mean labeling 
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     author = {R. Vasuki and P. Sugirtha and J. Venkateswari},
     title = {Super {Mean} {Labeling} of {Some} {Subdivision} {Graphs}},
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     year = {2017},
     language = {en},
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R. Vasuki; P. Sugirtha; J. Venkateswari. Super Mean Labeling of Some Subdivision Graphs. Kragujevac Journal of Mathematics, Tome 41 (2017) no. 2, p. 179 . http://geodesic.mathdoc.fr/item/KJM_2017_41_2_a1/