# Hereditary domination and independence parameters

Wayne Goddard; Teresa Haynes; Debra Knisley

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 2, page 239-248
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topWayne Goddard, Teresa Haynes, and Debra Knisley. "Hereditary domination and independence parameters." Discussiones Mathematicae Graph Theory 24.2 (2004): 239-248. <http://eudml.org/doc/270265>.

@article{WayneGoddard2004,

abstract = {For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.},

author = {Wayne Goddard, Teresa Haynes, Debra Knisley},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {domination; hereditary property; independence},

language = {eng},

number = {2},

pages = {239-248},

title = {Hereditary domination and independence parameters},

url = {http://eudml.org/doc/270265},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Wayne Goddard

AU - Teresa Haynes

AU - Debra Knisley

TI - Hereditary domination and independence parameters

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 2

SP - 239

EP - 248

AB - For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.

LA - eng

KW - domination; hereditary property; independence

UR - http://eudml.org/doc/270265

ER -

## References

top- [1] M. Borowiecki, I. Broere, M. Frick, P. Mihók and G. Semanišin, A survey of hereditary properties of graphs, Discuss. Math. Graph Theory 17 (1997) 5-50, doi: 10.7151/dmgt.1037. Zbl0902.05026
- [2] M. Borowiecki, D. Michalak and E. Sidorowicz, Generalized domination, independence and irredundance, Discuss. Math. Graph Theory 17 (1997) 143-153, doi: 10.7151/dmgt.1048. Zbl0904.05045
- [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: Advances in Graph Theory (Vishwa, 1991) 41-68.
- [4] M.R. Garey and D.S. Johnson, Computers and Intractability (W H Freeman, 1979).
- [5] J. Gimbel and P.D. Vestergaard, Inequalities for total matchings of graphs, Ars Combin. 39 (1995) 109-119. Zbl0837.05085
- [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, 1997). Zbl0890.05002
- [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.) Domination in Graphs: Advanced topics (Marcel Dekker, 1997).
- [8] T.W. Haynes and M.A. Henning, Path-free domination, J. Combin. Math. Combin. Comput. 33 (2000) 9-21.
- [9] S.M. Hedetniemi, S.T. Hedetniemi and D.F. Rall, Acyclic domination, Discrete Math. 222 (2000) 151-165, doi: 10.1016/S0012-365X(00)00012-1. Zbl0961.05052
- [10] D. Michalak, Domination, independence and irredundance with respect to additive induced-hereditary properties, Discrete Math., to appear.
- [11] C.M. Mynhardt, On the difference between the domination and independent domination number of cubic graphs, in: Graph Theory, Combinatorics, and Applications, Y. Alavi et al. eds, Wiley, 2 (1991) 939-947. Zbl0840.05038

## Citations in EuDML Documents

top- Vladimir D. Samodivkin, Domination with respect to nondegenerate properties: vertex and edge removal
- Vladimir D. Samodivkin, Domination with respect to nondegenerate and hereditary properties
- Vladimir D. Samodivkin, Upper bounds for the domination subdivision and bondage numbers of graphs on topological surfaces

## NotesEmbed ?

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