# The B-Domatic Number of a Graph

• Volume: 33, Issue: 4, page 747-757
• ISSN: 2083-5892

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## Abstract

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Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the counterpart of the b-chromatic number by giving an alternative definition of the maximality of a partition into dominating sets. We initiate the study of bd(G) by giving some properties and examples.

## How to cite

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Odile Favaron. "The B-Domatic Number of a Graph." Discussiones Mathematicae Graph Theory 33.4 (2013): 747-757. <http://eudml.org/doc/268011>.

@article{OdileFavaron2013,
abstract = {Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the counterpart of the b-chromatic number by giving an alternative definition of the maximality of a partition into dominating sets. We initiate the study of bd(G) by giving some properties and examples.},
author = {Odile Favaron},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {domatic number; adomatic number; b-domatic number; bchromatic number; idomatic number; partition; -domatic number; -chromatic number},
language = {eng},
number = {4},
pages = {747-757},
title = {The B-Domatic Number of a Graph},
url = {http://eudml.org/doc/268011},
volume = {33},
year = {2013},
}

TY - JOUR
AU - Odile Favaron
TI - The B-Domatic Number of a Graph
JO - Discussiones Mathematicae Graph Theory
PY - 2013
VL - 33
IS - 4
SP - 747
EP - 757
AB - Besides the classical chromatic and achromatic numbers of a graph related to minimum or minimal vertex partitions into independent sets, the b-chromatic number was introduced in 1998 thanks to an alternative definition of the minimality of such partitions. When independent sets are replaced by dominating sets, the parameters corresponding to the chromatic and achromatic numbers are the domatic and adomatic numbers d(G) and ad(G). We introduce the b-domatic number bd(G) as the counterpart of the b-chromatic number by giving an alternative definition of the maximality of a partition into dominating sets. We initiate the study of bd(G) by giving some properties and examples.
LA - eng
KW - domatic number; adomatic number; b-domatic number; bchromatic number; idomatic number; partition; -domatic number; -chromatic number
UR - http://eudml.org/doc/268011
ER -

## References

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