# Relations between the domination parameters and the chromatic index of a graph

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 3, page 615-627
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topWłodzimierz Ulatowski. "Relations between the domination parameters and the chromatic index of a graph." Discussiones Mathematicae Graph Theory 29.3 (2009): 615-627. <http://eudml.org/doc/270801>.

@article{WłodzimierzUlatowski2009,

abstract = {In this paper we show upper bounds for the sum and the product of the lower domination parameters and the chromatic index of a graph. We also present some families of graphs for which these upper bounds are achieved. Next, we give a lower bound for the sum of the upper domination parameters and the chromatic index. This lower bound is a function of the number of vertices of a graph and a new graph parameter which is defined here. In this case we also characterize graphs for which a respective equality holds.},

author = {Włodzimierz Ulatowski},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination; domination parameters; chromatic index},

language = {eng},

number = {3},

pages = {615-627},

title = {Relations between the domination parameters and the chromatic index of a graph},

url = {http://eudml.org/doc/270801},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Włodzimierz Ulatowski

TI - Relations between the domination parameters and the chromatic index of a graph

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 3

SP - 615

EP - 627

AB - In this paper we show upper bounds for the sum and the product of the lower domination parameters and the chromatic index of a graph. We also present some families of graphs for which these upper bounds are achieved. Next, we give a lower bound for the sum of the upper domination parameters and the chromatic index. This lower bound is a function of the number of vertices of a graph and a new graph parameter which is defined here. In this case we also characterize graphs for which a respective equality holds.

LA - eng

KW - domination; domination parameters; chromatic index

UR - http://eudml.org/doc/270801

ER -

## References

top- [1] M. Chellalia and L. Volkmann, Relations between the lower domination parameters and the chromatic number of a graph, Discrete Math. 274 (2004) 1-8, doi: 10.1016/S0012-365X(03)00093-1.
- [2] E.J. Cockayne, O. Favaron, C. Payan and A.G. Thomas, Contributions to the theory of domination, independence and irredundance in graphs, Discrete Math. 33 (1981) 249-258, doi: 10.1016/0012-365X(81)90268-5.
- [3] O. Favaron, Stability, domination and irredundance in a graph, J. Graph Theory 10 (1986) 429-438, doi: 10.1002/jgt.3190100402. Zbl0612.05056
- [4] T. Gallai, Über extreme Punkt-und Kantenmengen, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 2 (1959) 133-138. Zbl0094.36105
- [5] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Decker Inc., New York, 1998). Zbl0890.05002
- [6] D. König, Graphok és alkalmazásuk a determinánsok és a halmazok elméletére, Math. Termész. Ért. 34 (1916) 104-119. Zbl46.1451.03
- [7] D. König, Graphs and matrices, Mat. Fiz. Lapok 38 (1931) 116-119 (in Hungarian).
- [8] V.G. Vizing, On an estimate of the chromatic class of a p-graph, Metody Diskret. Analiz. 29 (1964) 25-30 (in Russian).

## NotesEmbed ?

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