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- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
- Subject
- Mathematics; Mathematics, general; Applications of Mathematics
- ISSN
- 0126-6705
- eISSN
- 2180-4206
- DOI
- 10.1007/s40840-018-0635-8
- Publisher site
- See Article on Publisher Site
Abstract
Let $$\gamma _\mathrm{tg}(G)$$ γ tg ( G ) denote the game total domination number of a graph G, and let G|v mean that a vertex v of G is declared to be already totally dominated. A graph G is total domination game critical if $$\gamma _\mathrm{tg}(G|v) < \gamma _\mathrm{tg}(G)$$ γ tg ( G | v ) < γ tg ( G ) holds for every vertex v in G. If $$\gamma _\mathrm{tg}(G) = k$$ γ tg ( G ) = k , then G is further called k- $$\gamma _\mathrm{tg}$$ γ tg -critical. In this paper, we prove that the circular ladder $$C_{4k} \,\square \,K_2$$ C 4 k □ K 2 is 4k- $$\gamma _{\mathrm{tg}}$$ γ tg -critical and that the Möbius ladder $$\mathrm{ML}_{2k}$$ ML 2 k is 2k- $$\gamma _{\mathrm{tg}}$$ γ tg -critical.
Journal
Bulletin of the Malaysian Mathematical Sciences Society – Springer Journals
Published: May 18, 2018