# On the Totalk-Domination in Graphs

Sergio Bermudo; Juan C. Hernández-Gómez; José M. Sigarreta

Discussiones Mathematicae Graph Theory (2018)

- Volume: 38, Issue: 1, page 301-317
- ISSN: 2083-5892

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topSergio 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 -

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