# Total outer-connected domination in trees

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 3, page 377-383
- ISSN: 2083-5892

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topJoanna Cyman. "Total outer-connected domination in trees." Discussiones Mathematicae Graph Theory 30.3 (2010): 377-383. <http://eudml.org/doc/270887>.

@article{JoannaCyman2010,

abstract = {Let G = (V,E) be a graph. Set D ⊆ V(G) is a total outer-connected dominating set of G if D is a total dominating set in G and G[V(G)-D] is connected. The total outer-connected domination number of G, denoted by $γ_\{tc\}(G)$, is the smallest cardinality of a total outer-connected dominating set of G. We show that if T is a tree of order n, then $γ_\{tc\}(T) ≥ ⎡2n/3⎤$. Moreover, we constructively characterize the family of extremal trees T of order n achieving this lower bound.},

author = {Joanna Cyman},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total outer-connected domination number; domination number},

language = {eng},

number = {3},

pages = {377-383},

title = {Total outer-connected domination in trees},

url = {http://eudml.org/doc/270887},

volume = {30},

year = {2010},

}

TY - JOUR

AU - Joanna Cyman

TI - Total outer-connected domination in trees

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 3

SP - 377

EP - 383

AB - Let G = (V,E) be a graph. Set D ⊆ V(G) is a total outer-connected dominating set of G if D is a total dominating set in G and G[V(G)-D] is connected. The total outer-connected domination number of G, denoted by $γ_{tc}(G)$, is the smallest cardinality of a total outer-connected dominating set of G. We show that if T is a tree of order n, then $γ_{tc}(T) ≥ ⎡2n/3⎤$. Moreover, we constructively characterize the family of extremal trees T of order n achieving this lower bound.

LA - eng

KW - total outer-connected domination number; domination number

UR - http://eudml.org/doc/270887

ER -

## References

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- [4] J.H. Hattingh, E. Jonck, E.J. Joubert and A.R. Plummer, Total Restrained Domination in Trees, Discrete Math. 307 (2007) 1643-1650, doi: 10.1016/j.disc.2006.09.014. Zbl1132.05044
- [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
- [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011

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