Skip to main content

Research Repository

Advanced Search

Perfect graphs of strong domination and independent strong domination

Zverovich, V. E.; Rautenbach, D.; Zverovich, Vadim

Authors

V. E. Zverovich

D. Rautenbach



Abstract

Let γ(G), i(G), γs(G) and is(G) denote the domination number, the independent domination number, the strong domination number and the independent strong domination number of a graph G, respectively. A graph G is called γi-perfect (domination perfect) if γ(H) = i(H), for every induced subgraph H of G. The classes of γγs-perfect, γsis-perfect, iis-perfect and γis-perfect graphs are defined analogously. In this paper we present a number of characterization results on the above classes of graphs. For example, characterizations of K4-free γsis-perfect graphs and triangle-free γis-perfect graphs are given. Moreover, the strong dominating set and independent strong dominating set problems as well as the weak dominating set and independent weak dominating set problems are shown to be NP-complete on a class of graphs. Several problems and conjectures are proposed. © 2001 Elsevier Science B.V. All rights reserved.

Citation

Zverovich, V. E., Rautenbach, D., & Zverovich, V. (2001). Perfect graphs of strong domination and independent strong domination. Discrete Mathematics, 226(1-3), 297-311. https://doi.org/10.1016/S0012-365X%2800%2900116-3

Journal Article Type Article
Publication Date Jan 1, 2001
Journal Discrete Mathematics
Print ISSN 0012-365X
Publisher Elsevier
Peer Reviewed Not Peer Reviewed
Volume 226
Issue 1-3
Pages 297-311
DOI https://doi.org/10.1016/S0012-365X%2800%2900116-3
Keywords domination, strong domination, independent strong domination, perfect, forbidden induced subgraph characterization, complexity
Public URL https://uwe-repository.worktribe.com/output/1088298
Publisher URL http://dx.doi.org/10.1016/S0012-365X(00)00116-3