Geodesic
On γ-labelings of trees
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 363-383.

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Let G be a graph of order n and size m. A γ-labeling of G is a one-to-one function f:V(G) → 0,1,2,...,m that induces a labeling f': E(G) → 1,2,...,m of the edges of G defined by f'(e) = |f(u)-f(v)| for each edge e = uv of G. The value of a γ-labeling f is val(f) = Σ_e ∈ E(G)f'K(e). The maximum value of a γ-labeling of G is defined as
Keywords: γ-labeling, value of a γ-labeling 
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Chartrand, Gary; Erwin, David; VanderJagt, Donald; Zhang, Ping. On γ-labelings of trees. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 3, pp. 363-383. http://geodesic.mathdoc.fr/item/DMGT_2005_25_3_a13/

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