Matching-Type Image-Labelings of Trees

Vertex Equitable Labelings of Transformed Trees

Distance three labelings of trees

An L(2, 1, 1)-labeling of a graph G assigns nonnegative integers to the vertices of G in such a way that labels of adjacent vertices differ by at least two, while vertices that are at distance at most three are assigned different labels. The maximum label used is called the span of the labeling, and the aim is to minimize this value. We show that the minimum span of an L(2, 1, 1)-labeling of a ...

On γ-labelings of trees

Let G be a graph of order n and size m. A γ-labeling of G is a oneto-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 valmax(G) = max{val(f) : f is a γ-labelin...

Distance Constrained Labelings of Trees

An H(p, q)-labeling of a graph G is a vertex mapping f : VG → VH such that the distance (in the graph H) of f(u) and f(v) is at least p (at least q) if the vertices u and v are adjacent in G (are at distance two in G, respectively). This notion generalizes the notions of L(p, q)and C(p, q)-labelings of graphs studied as a graph model of the Frequency Assignment Problem. We study the computation...

vertex equitable labelings of transformed trees

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