Let G be a simple graph of order n. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. Motivated by work of Cockayne et al. (1991) and Cockayne and Mynhardt (1989), we investigate the maximum value of the product of th
Independent domination in finitely defined classes of graphs
β Scribed by R. Boliac; V. Lozin
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 264 KB
- Volume
- 301
- Category
- Article
- ISSN
- 0304-3975
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β¦ Synopsis
We study the independent dominating set problem restricted to graph classes deΓΏned by ΓΏnitely many forbidden induced subgraphs. The main result is two su cient conditions for the problem to be NP-hard in a ΓΏnitely deΓΏned class of graphs. We conjecture that those conditions are also necessary and describe several classes of graphs verifying the conjecture.
π SIMILAR VOLUMES
Let Ξ±(G), Ξ³(G), and i(G) be the independence number, the domination number, and the independent domination number of a graph G, respectively. For any k β₯ 0, we define the following hereditary classes: Ξ±i where ISub(G) is the set of all induced subgraphs of a graph G. In this article, we present a f
## Abstract In this paper, we show that a Cayley graph for an abelian group has an independent perfect domination set if and only if it is a covering graph of a complete graph. As an application, we show that the hypercube __Q~n~__ has an independent perfect domination set if and only if __Q~n~__ i