On γ-labelings of trees
Gary Chartrand, David Erwin, Donald W. VanderJagt, Ping Zhang (2005)
Discussiones Mathematicae Graph Theory
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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 . The maximum value of a γ-labeling of G is defined as ; while the minimum value of a γ-labeling of G is ; The values and are determined for double stars . We present characterizations of connected graphs G of order n for which...