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Let G be a connected graph and let c : V (G) → {1, 2,. .. , k} be a coloring of the vertices of G for some positive integer k (where adjacent vertices may be colored the same). The color code of a vertex v of G (with respect to c) is the ordered (k+1)-tuple code(v) = (a 0 , a 1 ,. .. , a k) where a 0 is the color assigned to v and for 1 ≤ i ≤ k, a i is the… (More)

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) = e∈E(G) f (e). The maximum value of a γ-labeling of G is defined as val max… (More)

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