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On the circular-l(2, 1)-labelling for strong products of paths and cycles

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5 Author(s)
Yuan Yan Tang ; Fac. of Sci. & Technol., Univ. of Macau, Macau, China ; Zehui Shao ; Fangnian Lang ; Xiaodong Xu
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Let k be a positive integer. A k-circular-L(2, 1)-labelling of a graph G is an assignment f from V(G) to {0, 1, ..., k-1} such that, for any two vertices u and v, |f(u) -f(v)|k ≥ 2 if u and v are adjacent, and |f(u) -f(v)|k ≥ 1 if u and v are at distance 2, where |x|k = min{|x|, k-|x|}. The minimum k such that G admits a k-circular-L(2, 1)-labelling is called the circular-L(2, 1)-labelling number (or just the σ-number) of G, denoted by σ(G). The exact values of σ(PmCn) and σ(CmCn) for some m and n have been determined in this study. Finally, it has been concluded that σ(CmCn) ≤ 13 for nm ≥ 220.

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Communications, IET  (Volume:8 ,  Issue: 5 )