A Roman dominating function on a graph G is a labeling f : V (G) -β {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. A set { f 1 , f 2 , . . . , f d } of Roman dominating functions on G with the property that called a Roman dominating family (of functions) on G. The maximu
The domatic number of block-cactus graphs
β Scribed by Dieter Rautenbach; Lutz Volkmann
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 449 KB
- Volume
- 187
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let Ξ³(G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [Proc. 9th Southeast Conf. on Combin., Graph Theory & Comp. (1978) 43-56] and BollobΓ‘s and Cock- ayne [J. Graph Theory (1979) 241-249] proved independently that Ξ³(G) < 2ir(G) for
For a positive integer k, a k-rainbow dominating function of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex rainbow dominating family (of functions) on G. The maximum number of functions in a k-rainbow dominating f