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Abstract
The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. Similarly we define the total domination multisubdivision number msd_t (G) of a graph G and we show that for any connected graph G of order at least two, msd_t (G) ≤ 3. We show that for trees the total domination multisubdivision number is equal to the known total domination subdivision number. We also determine the total domination multisubdivision number for some classes of graphs and characterize trees T with msd_t (T) = 1.
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Authors (4)
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Diana Avella-alaminos dr
- Universidad Nacional Aut´onoma de M´exico School of Science
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Rita Zuazua
- Universidad Nacional Aut´onoma de M´exico School of Science
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.7151/dmgt.1798
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- Category:
- Articles
- Type:
- artykuły w czasopismach recenzowanych i innych wydawnictwach ciągłych
- Published in:
-
Discussiones Mathematicae Graph Theory
no. 35,
edition 2,
pages 315 - 327,
ISSN: 1234-3099 - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- Avella-Alaminos D., Dettlaff M., Lemańska M., Zuazua R.: TOTAL DOMINATION MULTISUBDIVISION NUMBER OF A GRAPH// Discussiones Mathematicae Graph Theory. -Vol. 35., iss. 2 (2015), s.315-327
- DOI:
- Digital Object Identifier (open in new tab) 10.7151/dmgt.1798
- Verified by:
- Gdańsk University of Technology
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