TY - JOUR

T1 - L(p,q)-labelings of subdivisions of graphs

AU - Chang, Fei Huang

AU - Chia, Ma Lian

AU - Jiang, Shih Ang

AU - Kuo, David

AU - Liaw, Sheng Chyang

N1 - Publisher Copyright:
© 2020 Elsevier B.V.

PY - 2021/3/11

Y1 - 2021/3/11

N2 - 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).

AB - 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).

KW - (p, q)-total labeling

KW - L(p, q)-labeling

KW - Subdivision

UR - http://www.scopus.com/inward/record.url?scp=85098223911&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2020.12.019

DO - 10.1016/j.dam.2020.12.019

M3 - 期刊論文

AN - SCOPUS:85098223911

VL - 291

SP - 264

EP - 270

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

ER -