منابع مشابه
Radio labelings of distance graphs
for any two distinct vertices x and y, where d(x, y) is the distance between x and y in G. The radio k-labeling number rlk(G) of G is the minimum of maxx,y∈V (G) |f(x)− f(y)| over all radio k-labelings f of G. The study of radio k-labelings was initiated by Chartrand et al. [1], motivated by radio channel assignment problems with interference constraints. Except for paths [1, 3] and cycles [5],...
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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) = ...
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This paper introduces a generalization of the graph bandwidth parameter: for a graph G and an integer k ≤ diam(G), the k-level bandwidth B(G) of G is defined by B(G) = minγ max{|γ(x)−γ(y)|−d(x, y)+1 : x, y ∈ V (G), d(x, y) ≤ k}, the minimum being taken among all proper numberings γ of the vertices of G. We present general bounds on B(G) along with more specific results for k = 2 and the exact v...
متن کاملDistance Labelings on Random Power Law Graphs
Methods for answering distance queries on large graphs through a preprocessed data structure have a rich history of study. Recent evaluations on social and information networks have shown that there are very efficient landmark based labeling schemes on these networks, even for exact distances. However, it is unclear what are the essential properties of these networks that make short labelings p...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.06.024