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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Bouchemakh, Isma
University of Sciences and Technology Houari Boumediene (USTHB)
Electrical & Electronics Engineering

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Upper Broadcast Domination Number of Caterpillars with no Trunks Bouchouika, Sabrina; Bouchemakh, Isma; Sopena, Eric
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 12, No 2 (2024): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2024.12.2.6

Abstract

A broadcast on a graph G = (V,E) is a function f : V →{0,…,diam(G)} such that f(v) ≤ eG(v) for every vertex v ∈ V , where diam(G) denotes the diameter of G and eG(v) the eccentricity of v in G. Such a broadcast f is minimal if there does not exist any broadcast g≠f on G such that g(v) ≤ f(v) for all v ∈ V . The upper broadcast domination number of G is the maximum value of ∑ v∈V f(v) among all minimal broadcasts f on G for which each vertex of G is at distance at most f(v) from some vertex v with f(v) ≥ 1. In this paper, we study the minimal dominating broadcasts of caterpillars and give the exact value of the upper broadcast domination number of caterpillars with no trunks.
Co-Authors Bouchouika, Sabrina Sopena, Eric