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Abstract
In 2008, Hedetniemi et al. introduced the concept of (1,)-domination and obtained some interesting results for (1,2) -domination. Obviously every (1,1) -dominating set of a graph (known as 2-dominating set) is (1,2) -dominating; to distinguish these concepts, we define a proper (1,2) -dominating set of a graph as follows: a subset is a proper (1,2) -dominating set of a graph if is (1,2) -dominating and it is not a (1,1) -dominating set of a graph. In particular, we introduce proper (1,2) -domination parameters and study their relations with (1,2) -domination parameters and the classical domination numbers.
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Authors (4)
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Adrian Michalski
- Politechnika Rzeszowska
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Iwona Włoch
- Politechnika Rzeszowska
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Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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MATHEMATICAL METHODS IN THE APPLIED SCIENCES
no. 45,
pages 7050 - 7057,
ISSN: 0170-4214 - Language:
- English
- Publication year:
- 2022
- Bibliographic description:
- Michalski A., Włoch I., Dettlaff M., Lemańska M.: On proper (1,2)‐dominating sets in graphs// MATHEMATICAL METHODS IN THE APPLIED SCIENCES -Vol. 45,iss. 11 (2022), s.7050-7057
- DOI:
- Digital Object Identifier (open in new tab) 10.1002/mma.8223
- Verified by:
- Gdańsk University of Technology
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