Given a factoring of a graph, the factor domination number yr is the smallest number of nodes which dominate all factors. General results, mainly involving bounds on yr for factoring of arbitrary graphs, are presented, and some of these are generalizations of well known relationships. The special c
Simultaneous graph parameters: Factor domination and factor total domination
β Scribed by Peter Dankelmann; Michael A. Henning; Wayne Goddard; Renu Laskar
- Book ID
- 108113674
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 174 KB
- Volume
- 306
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Let Ξ³(__G__) be the domination number of a graph __G__. Reed 6 proved that every graph __G__ of minimum degree at least three satisfies Ξ³(__G__)ββ€β(3/8)|__G__|, and conjectured that a better upper bound can be obtained for cubic graphs. In this paper, we prove that a 2βedgeβconnected cu
## Abstract A vertex __x__ in a subset __X__ of vertices of an undericted graph is __redundant__ if its closed neighbourhood is contained in the union of closed neighborhoods of vertices of __X__ β {__x__}. In the context of a communications network, this means that any vertex that may receive comm
In this paper, we consider a variation of total domination in which we limit the ability of a vertex to dominate its neighbors in one of two ways: (a) Every vertex in the dominating set dominates exactly k of its neighbors. Graphs that have such dominating sets are characterized and a recognition al