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.
@article{bwmeta1.element.bwnjournal-article-dmgtv24i2bwm,
author = {Wayne Goddard and Teresa Haynes and Debra Knisley},
title = {Hereditary domination and independence parameters},
journal = {Discussiones Mathematicae Graph Theory},
volume = {24},
year = {2004},
pages = {239-248},
zbl = {1065.05069},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-dmgtv24i2bwm}
}
Wayne Goddard; Teresa Haynes; Debra Knisley. Hereditary domination and independence parameters. Discussiones Mathematicae Graph Theory, Tome 24 (2004) pp. 239-248. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-dmgtv24i2bwm/
[000] [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. | Zbl 0902.05026
[001] [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. | Zbl 0904.05045
[002] [3] M. Borowiecki and P. Mihók, Hereditary properties of graphs, in: Advances in Graph Theory (Vishwa, 1991) 41-68.
[003] [4] M.R. Garey and D.S. Johnson, Computers and Intractability (W H Freeman, 1979).
[004] [5] J. Gimbel and P.D. Vestergaard, Inequalities for total matchings of graphs, Ars Combin. 39 (1995) 109-119. | Zbl 0837.05085
[005] [6] T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, 1997). | Zbl 0890.05002
[006] [7] T.W. Haynes, S.T. Hedetniemi and P.J. Slater (eds.) Domination in Graphs: Advanced topics (Marcel Dekker, 1997).
[007] [8] T.W. Haynes and M.A. Henning, Path-free domination, J. Combin. Math. Combin. Comput. 33 (2000) 9-21.
[008] [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. | Zbl 0961.05052
[009] [10] D. Michalak, Domination, independence and irredundance with respect to additive induced-hereditary properties, Discrete Math., to appear.
[010] [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. | Zbl 0840.05038