(2,1)-Total labeling of planar graphs with large maximum degree

2011/05/10 by Yong Yu, Xin Zhang, Yu, Yong +5
Computer Science · #05C15 #Advanced Graph Theory Research #Combinatorics (math.CO) #Digital Image Processing Techniques #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.1105.1908

openalex publication_date 2011/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we prove that, for planar graph G with maximum degree Δ≥12 and d=2, the (2,1)-total labelling number λ₂^T(G) is at most Δ+2.

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