Abstract
The most famous open problem involving domination in graphs is Vizing's conjecture which states the domination number of the Cartesian product of any two graphs is at least as large as the product of their domination numbers. In this paper, we investigate a similar problem for total domination. In particular, we prove that the product of the total domination numbers of any nontrivial tree and any graph without isolated vertices is at most twice the total domination number of their Cartesian product, and we characterize the extremal graphs.
| Original language | English |
|---|---|
| Pages (from-to) | 63-69 |
| Number of pages | 7 |
| Journal | Graphs and Combinatorics |
| Volume | 21 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 2005 |
| Externally published | Yes |
Keywords
- Graph products
- Total domination
- Vizing's conjecture
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics