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| Titre: | On the upper global powerful alliance number in trees |
| Auteur(s): | Ouatiki, Saliha |
| Mots-clés: | Domination
Global powerful alliance
Trees |
| Date de publication: | 2020 |
| Editeur: | Charles Babbage Research Centre |
| Collection/Numéro: | Ars Combinatoria/ Vol.151 (2020);pp. 89-98 |
| Résumé: | Search
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Document details - On the upper global powerful alliance number in trees
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Document type
Article
Source type
Journal
ISSN
03817032
Ars CombinatoriaVolume 151, Pages 89 - 98July 2020
On the upper global powerful alliance number in trees
Dept of Mathematics, University of Boumerdes, Algeria
Abstract
For a graph G = (V,E), a set D ⊆ V is a dominating set if every vertex in V — D is either in D or has a neighbor in D. A dominating set D is a global offensive alliance (resp. a global defensive alliance) if for each vertex v in V — D (resp. v in í?) at least half the vertices from the closed neighborhood of v are in C A global powerful alliance is both global defensive and global offensive. The global powerful alliance number γpo(G) is the minimum cardinality of a global powerful alliance of G. It was shown in [1] that any tree T different from a star Sij, with order n ≥ 4, l leaves and s support vertices verifies γpo(T) ≤ 4n + 1 + s/6 . In this paper, we provide a constructive characterization of all extremal trees attaining this bound |
| URI/URL: | http://dlibrary.univ-boumerdes.dz:8080/handle/123456789/7168 |
| ISSN: | 03817032 |
| Collection(s) : | Publications Internationales
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