Geodesic
Total outer-connected domination in trees
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 377-383 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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.
Keywords: total outer-connected domination number, domination number 
@article{DMGT_2010_30_3_a1,
     author = {Cyman, Joanna},
     title = {Total outer-connected domination in trees},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {377--383},
     year = {2010},
     volume = {30},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a1/}
}
TY  - JOUR
AU  - Cyman, Joanna
TI  - Total outer-connected domination in trees
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2010
SP  - 377
EP  - 383
VL  - 30
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a1/
LA  - en
ID  - DMGT_2010_30_3_a1
ER  - 
%0 Journal Article
%A Cyman, Joanna
%T Total outer-connected domination in trees
%J Discussiones Mathematicae. Graph Theory
%D 2010
%P 377-383
%V 30
%N 3
%U http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a1/
%G en
%F DMGT_2010_30_3_a1
Cyman, Joanna. Total outer-connected domination in trees. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 3, pp. 377-383. http://geodesic.mathdoc.fr/item/DMGT_2010_30_3_a1/

[1] G. Chartrand and L. Leśniak, Graphs Digraphs (Wadsworth and Brooks/Cole, Monterey, CA, third edition, 1996).

[2] E.J. Cockayne, R.M. Dawes and S.T. Hedetniemi, Total domination in graphs, Networks 10 (1980) 211-219, doi: 10.1002/net.3230100304.

[3] G.S. Domke, J.H. Hattingh, M.A. Henning and L.R. Markus, Restrained domination in trees, Discrete Math. 211 (2000) 1-9, doi: 10.1016/S0012-365X(99)00036-9.

[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.

[5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).

[6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).