# A note on the domination number of a graph and its complement

Mathematica Bohemica (2001)

- Volume: 126, Issue: 1, page 63-65
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topMarcu, Dănuţ. "A note on the domination number of a graph and its complement." Mathematica Bohemica 126.1 (2001): 63-65. <http://eudml.org/doc/248850>.

@article{Marcu2001,

abstract = {If $G$ is a simple graph of size $n$ without isolated vertices and $\overline\{G\}$ is its complement, we show that the domination numbers of $G$ and $\overline\{G\}$ satisfy \[ \gamma (G) + \gamma (\overline\{G\}) \le \left\rbrace \begin\{array\}\{ll\}n-\delta + 2 \quad \text\{if\} \quad \gamma (G) > 3, \delta + 3 \quad \text\{if\} \quad \gamma (\overline\{G\}) > 3, \end\{array\}\right.\]
where $\delta $ is the minimum degree of vertices in $G$.},

author = {Marcu, Dănuţ},

journal = {Mathematica Bohemica},

keywords = {graphs; domination number; graph’s complement; domination number; complement},

language = {eng},

number = {1},

pages = {63-65},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A note on the domination number of a graph and its complement},

url = {http://eudml.org/doc/248850},

volume = {126},

year = {2001},

}

TY - JOUR

AU - Marcu, Dănuţ

TI - A note on the domination number of a graph and its complement

JO - Mathematica Bohemica

PY - 2001

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 126

IS - 1

SP - 63

EP - 65

AB - If $G$ is a simple graph of size $n$ without isolated vertices and $\overline{G}$ is its complement, we show that the domination numbers of $G$ and $\overline{G}$ satisfy \[ \gamma (G) + \gamma (\overline{G}) \le \left\rbrace \begin{array}{ll}n-\delta + 2 \quad \text{if} \quad \gamma (G) > 3, \delta + 3 \quad \text{if} \quad \gamma (\overline{G}) > 3, \end{array}\right.\]
where $\delta $ is the minimum degree of vertices in $G$.

LA - eng

KW - graphs; domination number; graph’s complement; domination number; complement

UR - http://eudml.org/doc/248850

ER -

## References

top- Graphes et Hypergraphes, Dunod, Paris, 1970. (1970) Zbl0213.25702MR0357173
- Graph Theory with Applications, Macmillan Press, 1976. (1976) MR0411988

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.