Zhang, Sumei; Wang, Jihui \(L(p,q)\)-labelling of planar graphs with high maximum degree. (Chinese. English summary) Zbl 1158.05336 J. Shandong Univ., Nat. Sci. 42, No. 4, 39-43 (2007). Summary: J.R. Griggs and R.K.-C. Yeh [SIAM J. Discrete Math. 5, No.4, 586–595 (1992; Zbl 0767.05080)]conjectured that \(\lambda(G;2,1) \leq \Delta^2\) for any simple graph. The \(L(p, q)\)-labelling number on planar graphs with high maximum degree is considered. It is proved that \(\lambda(G;p, q) \leq (2q-1)\Delta+6(p-q)\) for \(h_1\)-graph and \(\lambda(G;p, q) \leq (2q-1)\Delta+8p-6q-1\) for \(h_2\)-graph. MSC: 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C10 Planar graphs; geometric and topological aspects of graph theory 05C35 Extremal problems in graph theory Keywords:planar graph with high maximum degree; \(L(p,q)\)-labelling; maximum degree Citations:Zbl 0767.05080 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{J. Wang}, J. Shandong Univ., Nat. Sci. 42, No. 4, 39--43 (2007; Zbl 1158.05336)