L(p,q)-labelings of subdivisions of graphs

Fei Huang Chang, Ma Lian Chia, Shih Ang Jiang, David Kuo, Sheng Chyang Liaw

Research output: Contribution to journalArticlepeer-review

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Given a graph G and a function h from E(G) to N, the h-subdivision of G, denoted by G(h), is the graph obtained from G by replacing each edge uv in G with a path P:uxuv1xuv2…xuvn−1v, where n=h(uv). When h(e)=c is a constant for all e∈E(G), we use G(c) to replace G(h). For a given graph G, an L(p,q)-labeling of G is a function f from the vertex set V(G) to the set of all nonnegative integers such that f(u)−f(v)≥p if dG(u,v)=1, and f(u)−f(v)≥q if dG(u,v)=2. A k-L(p,q)-labeling is an L(p,q)-labeling such that no label is greater than k. The L(p,q)-labeling number of G, denoted by λp,q(G), is the smallest number k such that G has a k-L(p,q) -labeling. We study the L(p,q)-labeling numbers of subdivisions of graphs in this paper. We prove that λp,q(G(3))=p+(Δ−1)q when p≥2q and [Formula presented], and show that λp,q(G(h))=p+(Δ−1)q when p≥2q and [Formula presented], where h is a function from E(G) to N so that h(e)≥3 for all e∈E(G).

Original languageEnglish
Pages (from-to)264-270
Number of pages7
JournalDiscrete Applied Mathematics
StatePublished - 11 Mar 2021


  • (p, q)-total labeling
  • L(p, q)-labeling
  • Subdivision


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