Distance Two Labeling of Direct Product of Paths and Cycles
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Date
2013
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arXiv preprint
Abstract
Suppose that [n] = {0, 1, 2, ..., n} is a set of non-negative integers and h, k ∈ [n]. The L(h, k)-labeling of graph G is the function l : V (G) → [n] such that |l(u) − l(v)| ≥ h if the distance d(u, v) between u and v is one and |l(u) − l(v)| ≥ k if the distance d(u, v) is two. Let L(V (G)) = {l(v) : v ∈ V (G)} and let p be the maximum value of L(V (G)). Then p is called k h−number of G if p is the least possible member of [n] such that G maintains an L(h, k)−labeling. In this paper, we establish 1 1− numbers of Pm × Cn graphs for all m ≥ 2 and n ≥ 3.
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Citation
Adefokun, T. C. and Ajayi, D. O. (2013). Distance Two Labeling of Direct Product of Paths and Cycles. arXiv preprint.