Minus total domination in graphs

Hua Ming Xing; Hai-Long Liu

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 4, page 861-870
  • ISSN: 0011-4642

Abstract

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A three-valued function f V → { - 1 , 0 , 1 } defined on the vertices of a graph G = ( V , E ) is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every v ∈ V , f ( N ( v ) ) ≥ 1 , where N ( v ) consists of every vertex adjacent to v . The weight of an MTDF is f ( V ) = ∑ f ( v ) , over all vertices v ∈ V . The minus total domination number of a graph G , denoted γ t - ( G ) , equals the minimum weight of an MTDF of G . In this paper, we discuss some properties of minus total domination on a graph G and obtain a few lower bounds for γ t - ( G ) .

How to cite

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Xing, Hua Ming, and Liu, Hai-Long. "Minus total domination in graphs." Czechoslovak Mathematical Journal 59.4 (2009): 861-870. <http://eudml.org/doc/37963>.

@article{Xing2009,
abstract = {A three-valued function $f\: V\rightarrow \lbrace -1,0,1\rbrace $ defined on the vertices of a graph $G=(V,E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v\in V$, $f(N(v))\ge 1$, where $N(v)$ consists of every vertex adjacent to $v$. The weight of an MTDF is $f(V)=\sum f(v)$, over all vertices $v\in V$. The minus total domination number of a graph $G$, denoted $\gamma _t^\{-\}(G)$, equals the minimum weight of an MTDF of $G$. In this paper, we discuss some properties of minus total domination on a graph $G$ and obtain a few lower bounds for $\gamma _t^\{-\}(G)$.},
author = {Xing, Hua Ming, Liu, Hai-Long},
journal = {Czechoslovak Mathematical Journal},
keywords = {minus domination; total domination; minus total domination; minus domination; total domination; minus total domination},
language = {eng},
number = {4},
pages = {861-870},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Minus total domination in graphs},
url = {http://eudml.org/doc/37963},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Xing, Hua Ming
AU - Liu, Hai-Long
TI - Minus total domination in graphs
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 4
SP - 861
EP - 870
AB - A three-valued function $f\: V\rightarrow \lbrace -1,0,1\rbrace $ defined on the vertices of a graph $G=(V,E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v\in V$, $f(N(v))\ge 1$, where $N(v)$ consists of every vertex adjacent to $v$. The weight of an MTDF is $f(V)=\sum f(v)$, over all vertices $v\in V$. The minus total domination number of a graph $G$, denoted $\gamma _t^{-}(G)$, equals the minimum weight of an MTDF of $G$. In this paper, we discuss some properties of minus total domination on a graph $G$ and obtain a few lower bounds for $\gamma _t^{-}(G)$.
LA - eng
KW - minus domination; total domination; minus total domination; minus domination; total domination; minus total domination
UR - http://eudml.org/doc/37963
ER -

References

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