The L(2, 1)-Labeling Problem on Graphs

@article{Chang1996TheL1,
  title={The L(2, 1)-Labeling Problem on Graphs},
  author={Gerard J. Chang and David Kuo},
  journal={SIAM J. Discrete Math.},
  year={1996},
  volume={9},
  pages={309-316}
}
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. 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. In this paper, we give exact formulas of λ(G ∪H) and λ(G + H). We also prove that λ(G) ≤ ∆ + ∆ for any graph G of maximum degree ∆. For OSF-chordal graphs, the upper bound… CONTINUE READING
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