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Abstract
A setDof vertices of a graphG= (VG,EG) is a dominating set ofGif every vertexinVG−Dis adjacent to at least one vertex inD. The domination number (upper dominationnumber, respectively) ofG, denoted byγ(G) (Γ(G), respectively), is the cardinality ofa smallest (largest minimal, respectively) dominating set ofG. A subsetD⊆VGis calleda certified dominating set ofGifDis a dominating set ofGand every vertex inDhas eitherzero or at least two neighbors inVG−D. The cardinality of a smallest (largest minimal,respectively) certified dominating set ofGis called the certified (upper certified, respectively)domination number ofGand is denoted byγcer(G) (Γcer(G), respectively). In this paperrelations between domination, upper domination, certified domination and upper certifieddomination numbers of a graph are studied
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Authors (6)
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Jerzy Topp
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Mateusz Miotk mgr inż.
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Radosław Ziemann
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Paweł Żyliński
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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Opuscula Mathematica
no. 39,
pages 815 - 827,
ISSN: 1232-9274 - Language:
- English
- Publication year:
- 2019
- Bibliographic description:
- Dettlaff M., Lemańska M., Topp J., Miotk M., Ziemann R., Żyliński P.: Graphs with equal domination and certified domination numbers// Opuscula Mathematica -Vol. 39,iss. 6 (2019), s.815-827
- DOI:
- Digital Object Identifier (open in new tab) 10.7494/opmath.2019.39.6.815
- Verified by:
- Gdańsk University of Technology
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