This work deals with the domination numbers of generalized de Bruijn digraphs and generalized Kautz digraphs. Dominating sets for digraphs are not familiar compared with dominating sets for undirected graphs. Whereas dominating sets for digraphs have more applications than those for undirected graph
The total domination and total bondage numbers of extended de Bruijn and Kautz digraphs
β Scribed by Jia Huang; Jun-Ming Xu
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 218 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Motivated by the problem of designing large packet radio networks, we show that the Kautz and de Bruijn digraphs with inβ and outdegree __d__ have arcβchromatic index __2d__. In order to do this, we introduce the concept of even 1βfactorizations. An even 1βfactor of a digraph is a spann
## Abstract We prove that __m__ββ€βΞ (__n__βββΞ³~t~) for every graph each component of which has order at least 3 of order __n__, size __m__, total domination number Ξ³~t~, and maximum degree Ξββ₯β3. Β© 2005 Wiley Periodicals, Inc. J Graph Theory 49: 285β290, 2005
## Abstract The proof of the main theorem in the paper [1] is incorrect as it is missing an important case. Here we complete the proof by giving the missing case. Β© 2007 Wiley Periodicals, Inc. J Graph Theory 54: 350β353, 2007