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Abstract
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.
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Authors (4)
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Maria Jose Souto-Salorio prof
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Adriana Dapena prof.
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Francisco Vazquez-Araujo dr
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.3390/math9121325
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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Mathematics
no. 9,
ISSN: 2227-7390 - Language:
- English
- Publication year:
- 2021
- Bibliographic description:
- Lemańska M., Souto-Salorio M. J., Dapena A., Vazquez-Araujo F.: Isolation Number versus Domination Number of Trees// Mathematics -Vol. 9,iss. 12 (2021),
- DOI:
- Digital Object Identifier (open in new tab) 10.3390/math9121325
- Verified by:
- Gdańsk University of Technology
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