Geodesic
Super mean number of a graph
Kragujevac Journal of Mathematics, Tome 36 (2012) no. 1, p. 93

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G$ be a graph and let $f:V(G)\rightarrow \{1,2,\dots,n\}$ be a function such that the label of the edge $uv$ is $\frac{f(u)+f(v)}{2}$ or $\frac{f(u)+f(v)+1}{2}$ according as $f(u)+f(v)$ is even or odd and $f(V(G))\cup \{f^*(e):e\in E(G)\}\subseteq \{1,2,\dots,n\}$. If $n$ is the smallest positive integer satisfying these conditions together with the condition that all the vertex and edge labels are distinct and there is no common vertex and edge labels, then $n$ is called the super mean number of a graph $G$ and it is denoted by $S_m(G)$. In this paper, we find the bounds for super mean number of some standard graphs.
Classification : 05C78
Keywords: Labeling, super mean graph, super mean number 
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A. Nagarajan; R. Vasuki; S. Arockiaraj. Super mean number of a graph. Kragujevac Journal of Mathematics, Tome 36 (2012) no. 1, p. 93 . http://geodesic.mathdoc.fr/item/KJM_2012_36_1_a10/