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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