# Total Domination Multisubdivision Number of a Graph

Diana Avella-Alaminos; Magda Dettlaff; Magdalena Lemańska; Rita Zuazua

Discussiones Mathematicae Graph Theory (2015)

- Volume: 35, Issue: 2, page 315-327
- ISSN: 2083-5892

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topDiana Avella-Alaminos, et al. "Total Domination Multisubdivision Number of a Graph." Discussiones Mathematicae Graph Theory 35.2 (2015): 315-327. <http://eudml.org/doc/271098>.

@article{DianaAvella2015,

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 msdγt (G) of a graph G and we show that for any connected graph G of order at least two, msdγt (G) ≤ 3. We show that for trees the total domination multisubdi- vision 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 msdγt (T) = 1.},

author = {Diana Avella-Alaminos, Magda Dettlaff, Magdalena Lemańska, Rita Zuazua},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {(total) domination; (total) domination subdivision number; (total) domination multisubdivision number; trees; total domination; total domination subdivision number; total domination multisubdivision number},

language = {eng},

number = {2},

pages = {315-327},

title = {Total Domination Multisubdivision Number of a Graph},

url = {http://eudml.org/doc/271098},

volume = {35},

year = {2015},

}

TY - JOUR

AU - Diana Avella-Alaminos

AU - Magda Dettlaff

AU - Magdalena Lemańska

AU - Rita Zuazua

TI - Total Domination Multisubdivision Number of a Graph

JO - Discussiones Mathematicae Graph Theory

PY - 2015

VL - 35

IS - 2

SP - 315

EP - 327

AB - 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 msdγt (G) of a graph G and we show that for any connected graph G of order at least two, msdγt (G) ≤ 3. We show that for trees the total domination multisubdi- vision 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 msdγt (T) = 1.

LA - eng

KW - (total) domination; (total) domination subdivision number; (total) domination multisubdivision number; trees; total domination; total domination subdivision number; total domination multisubdivision number

UR - http://eudml.org/doc/271098

ER -

## References

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- [8] T.W. Haynes, M.A. Henning and L.S. Hopkins, Total domination subdivision num- bers of trees, Discrete Math. 286 (2004) 195-202. doi:10.1016/j.disc.2004.06.004[Crossref]
- [9] H. Karami, A. Khodkar, R. Khoeilar and S.M. Sheikholeslami, Trees whose total domination subdivision number is one, Bull. Inst. Combin. Appl. 53 (2008) 56-57. Zbl1168.05050
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