# On the total restrained domination number of direct products of graphs

Wai Chee Shiu; Hong-Yu Chen; Xue-Gang Chen; Pak Kiu Sun

Discussiones Mathematicae Graph Theory (2012)

- Volume: 32, Issue: 4, page 629-641
- ISSN: 2083-5892

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topWai Chee Shiu, et al. "On the total restrained domination number of direct products of graphs." Discussiones Mathematicae Graph Theory 32.4 (2012): 629-641. <http://eudml.org/doc/270917>.

@article{WaiCheeShiu2012,

abstract = {Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V∖S is adjacent to a vertex in S as well as to another vertex in V∖S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by $γ_r^t(G)$, is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.},

author = {Wai Chee Shiu, Hong-Yu Chen, Xue-Gang Chen, Pak Kiu Sun},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {total domination number; total restrained domination number; direct product of graphs},

language = {eng},

number = {4},

pages = {629-641},

title = {On the total restrained domination number of direct products of graphs},

url = {http://eudml.org/doc/270917},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Wai Chee Shiu

AU - Hong-Yu Chen

AU - Xue-Gang Chen

AU - Pak Kiu Sun

TI - On the total restrained domination number of direct products of graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2012

VL - 32

IS - 4

SP - 629

EP - 641

AB - Let G = (V,E) be a graph. A total restrained dominating set is a set S ⊆ V where every vertex in V∖S is adjacent to a vertex in S as well as to another vertex in V∖S, and every vertex in S is adjacent to another vertex in S. The total restrained domination number of G, denoted by $γ_r^t(G)$, is the smallest cardinality of a total restrained dominating set of G. We determine lower and upper bounds on the total restrained domination number of the direct product of two graphs. Also, we show that these bounds are sharp by presenting some infinite families of graphs that attain these bounds.

LA - eng

KW - total domination number; total restrained domination number; direct product of graphs

UR - http://eudml.org/doc/270917

ER -

## References

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