On the Totalk-Domination in Graphs

Sergio Bermudo, Juan C. Hernández-Gómez, and José M. Sigarreta. "On the Totalk-Domination in Graphs." Discussiones Mathematicae Graph Theory 38.1 (2018): 301-317. <http://eudml.org/doc/288443>.

@article{SergioBermudo2018,
abstract = {Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination parameters of the graph.},
author = {Sergio Bermudo, Juan C. Hernández-Gómez, José M. Sigarreta},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {k-domination; total k-domination; k-tuple domination; k-tuple total domination},
language = {eng},
number = {1},
pages = {301-317},
title = {On the Totalk-Domination in Graphs},
url = {http://eudml.org/doc/288443},
volume = {38},
year = {2018},
}

TY - JOUR
AU - Sergio Bermudo
AU - Juan C. Hernández-Gómez
AU - José M. Sigarreta
TI - On the Totalk-Domination in Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2018
VL - 38
IS - 1
SP - 301
EP - 317
AB - Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination parameters of the graph.
LA - eng
KW - k-domination; total k-domination; k-tuple domination; k-tuple total domination
UR - http://eudml.org/doc/288443
ER -