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Abstract
Given a graph G and a function h from E(G) to N, the hsubdivision of G, denoted by G_{(h)}, is the graph obtained from G by replacing each edge uv in G with a path P:ux_{uv}^{1}x_{uv}^{2}…x_{uv}^{n−1}v, 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 d_{G}(u,v)=1, and f(u)−f(v)≥q if d_{G}(u,v)=2. A kL(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 λ_{p,q}(G), is the smallest number k such that G has a kL(p,q) labeling. We study the L(p,q)labeling numbers of subdivisions of graphs in this paper. We prove that λ_{p,q}(G_{(3)})=p+(Δ−1)q when p≥2q and [Formula presented], and show that λ_{p,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 

Pages (fromto)  264270 
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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 1 Finished

Design and Analysis of Algorithms for (T,R) Broadcast Domination Problems(2/2)
1/08/18 → 31/07/19
Project: Research