Distance three labelings of 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 ...

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

Distance magic labelings of graphs

As a natural extension of previously defined graph labelings, we introduce in this paper a new magic labeling whose evaluation is based on the neighbourhood of a vertex. We define a 1-vertex-magic vertex labeling of a graph with v vertices as a bijection f taking the vertices to the integers 1, 2, . . . , v with the property that there is a constant k such that at any vertex x, ∑ y∈N(x) f(y) = ...

Distance-two labelings of digraphs

For positive integers j ≥ k, an L(j, k)-labeling of a digraph D is a function f from V (D) into the set of nonnegative integers such that |f(x) − f(y)| ≥ j if x is adjacent to y in D and |f(x) − f(y)| ≥ k if x is of distant two to y in D. Elements of the image of f are called labels. The L(j, k)-labeling problem is to determine the ~λj,knumber ~λj,k(D) of a digraph D, which is the minimum of th...