| Autor: |
Magdalena Lemańska, María José Souto-Salorio, Adriana Dapena, Francisco J. Vazquez-Araujo |
| Jazyk: |
angličtina |
| Rok vydání: |
2021 |
| Předmět: |
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| Zdroj: |
Mathematics, Vol 9, Iss 12, p 1325 (2021) |
| Druh dokumentu: |
article |
| ISSN: |
2227-7390 |
| DOI: |
10.3390/math9121325 |
| Popis: |
If G=(VG,EG) is a graph of order n, we call S⊆VG an isolating set if the graph induced by VG−NG[S] contains no edges. The minimum cardinality of an isolating set of G is called the isolation number of G, and it is denoted by ι(G). It is known that ι(G)≤n3 and the bound is sharp. A subset S⊆VG is called dominating in G if NG[S]=VG. The minimum cardinality of a dominating set of G is the domination number, and it is denoted by γ(G). In this paper, we analyze a family of trees T where ι(T)=γ(T), and we prove that ι(T)=n3 implies ι(T)=γ(T). Moreover, we give different equivalent characterizations of such graphs and we propose simple algorithms to build these trees from the connections of stars. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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