Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/33302
Title: The L (2, 1)-labeling on graphs and the frequency assignment problem
Authors: Shao, Z
Yeh, RK
Zhang, D 
Keywords: Channel assignment
L (2, 1)-labeling
Total graph
Issue Date: 2008
Source: Applied mathematics letters, 2008, v. 21, no. 1, p. 37-41 How to cite?
Journal: Applied Mathematics Letters 
Abstract: An L (2, 1)-labeling of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that | f (x) - f (y) | ≥ 2 if d (x, y) = 1 and | f (x) - f (y) | ≥ 1 if d (x, y) = 2, where d (x, y) denotes the distance between x and y in G. The L (2, 1)-labeling number λ (G) of G is the smallest number k such that G has an L (2, 1)-labeling with max {f (v) : v ∈ V (G)} = k. Griggs and Yeh conjecture that λ (G) ≤ Δ2 for any simple graph with maximum degree Δ ≥ 2. In this work, we consider the total graph and derive its upper bound of λ (G). The total graph plays an important role in other graph coloring problems. Griggs and Yeh's conjecture is true for the total graph in some cases.
URI: http://hdl.handle.net/10397/33302
ISSN: 0893-9659
DOI: 10.1016/j.aml.2006.08.029
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