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Abstract
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 language | English |
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Pages (from-to) | 264-270 |
Number of pages | 7 |
Journal | Discrete Applied Mathematics |
Volume | 291 |
DOIs | |
State | Published - 11 Mar 2021 |
Keywords
- (p, q)-total labeling
- L(p, q)-labeling
- Subdivision
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Dive into the research topics of 'L(p,q)-labelings of subdivisions of graphs'. Together they form a unique fingerprint.Projects
- 1 Finished
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Design and Analysis of Algorithms for (T,R) Broadcast Domination Problems(2/2)
1/08/18 → 31/07/19
Project: Research