Multilevel Bandwidth and Radio Labelings of Graphs
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چکیده
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 value for k = diam(G). We also exhibit relations between the k-level bandwidth and radio k-labelings of graphs from which we derive a upper bound for the radio number of an arbitrary graph.
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تاریخ انتشار 2008