On L(p,q)-labelling of planar graphs without cycles of length four

Jianfeng Hou, Yindong Jin, Heng Li, Lianying Miao and Qian Zhao

Applied Mathematics and Computation, 2023, vol. 446, issue C

Abstract: Let p,q be integers with p≥q≥0 and let G be a graph. A k−L(p,q)−labeling of G is a function φ:V(G)→{0,1,…,k} such that |φ(x)−φ(y)|≥p if xy∈E(G), and |φ(x)−φ(y)|≥q if x and y have at least one common neighbor in G. Suppose that G is a planar graph with maximum degree Δ, and without cycles of length four. We show that λp,q(G)≤(2q−1)Δ+8p+10q−9, which improves the bound given by Zhu, Hou, Chen and Lv [The L(p,q)-labelling of planar graphs without 4-cycles, Discrete Appl. Math. 162 (2014) 355–363].

Keywords: L(p,q)-coloring; Planar graph; Cycle (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:446:y:2023:i:c:s009630032300053x

DOI: 10.1016/j.amc.2023.127884

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