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 , 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 . Moreover, we constructively characterize the family of extremal trees T of order n achieving this lower bound.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1500,
author = {Joanna Cyman},
title = {Total outer-connected domination in trees},
journal = {Discussiones Mathematicae Graph Theory},
volume = {30},
year = {2010},
pages = {377-383},
zbl = {1217.05059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1500}
}
Joanna Cyman. Total outer-connected domination in trees. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 377-383. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1500/
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