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

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

1 引文 斯高帕斯（Scopus）

## 摘要

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).

原文 ???core.languages.en_GB??? 264-270 7 Discrete Applied Mathematics 291 https://doi.org/10.1016/j.dam.2020.12.019 已出版 - 11 3月 2021

## 指紋

• ### 設計與探討圖形上有(t,r)關擴散控制的演算法(2/2)

Liaw, S.

1/08/1831/07/19

研究計畫: Research