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Article Dans Une Revue Discrete Applied Mathematics Année : 2018

On the Broadcast Independence Number of Caterpillars

Messaouda Ahmane
  • Fonction : Auteur
Isma Bouchemakh
  • Fonction : Auteur

Résumé

Let $G$ be a simple undirected graph. A broadcast on $G$ is a function $f : V(G)\rightarrow\mathbb{N}$ such that $f(v)\le e_G(v)$ holds for every vertex $v$ of $G$, where $e_G(v)$ denotes the eccentricity of $v$ in $G$, that is, the maximum distance from $v$ to any other vertex of $G$. The cost of $f$ is the value ${\rm cost}(f)=\sum_{v\in V(G)}f(v)$. A broadcast $f$ on $G$ is independent if for every two distinct vertices $u$ and $v$ in $G$, $d_G(u,v)>\max\{f(u),f(v)\}$, where $d_G(u,v)$ denotes the distance between $u$ and $v$ in $G$. The broadcast independence number of $G$ is then defined as the maximum cost of an independent broadcast on $G$. In this paper, we study independent broadcasts of caterpillars and give an explicit formula for the broadcast independence number of caterpillars having no pair of adjacent trunks, a trunk being an internal spine vertex with degree~2.
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Dates et versions

hal-01421875 , version 1 (23-12-2016)
hal-01421875 , version 2 (15-01-2018)

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Messaouda Ahmane, Isma Bouchemakh, Eric Sopena. On the Broadcast Independence Number of Caterpillars. Discrete Applied Mathematics, 2018, 244, pp.20-35. ⟨hal-01421875v2⟩

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