Abstract
Recently, Azarija et al. (Electron J Combin:1.19, 2017) considered the prism G□ K2 of a graph G and showed that γt(G□ K2) = 2 γ(G) if G is bipartite, where γt(G) and γ(G) are the total domination number and the domination number of G. In this note, we give a simple proof and observe that there are similar results for other pairs of parameters. We also answer a question from that paper and show that for all graphs γt(G□K2)≥43γ(G), and this bound is tight.
Original language | English |
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Pages (from-to) | 14-20 |
Number of pages | 7 |
Journal | Journal of Combinatorial Optimization |
Volume | 35 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Jan 2018 |
Keywords
- Domination
- Prisms
- Total domination
ASJC Scopus subject areas
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics