| Title: | How long can one bluff in the domination game? |
|---|
| Authors: | ID Brešar, Boštjan (Author)
ID Dorbec, Paul (Author)
ID Klavžar, Sandi (Author)
ID Košmrlj, Gašper (Author) |
|---|
| Files: |  Discussiones_Mathematicae_Graph_Theory_2017_Bresar_et_al._How_long_can_one_bluff_in_the_domination_game.pdf (56,60 KB)
MD5: E2E21DDAD32086F0B202FAFD568E19EF
 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1899
|
|---|
| Language: | English |
|---|
| Work type: | Scientific work |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FNM - Faculty of Natural Sciences and Mathematics
|
|---|
| Abstract: | The domination game is played on an arbitrary graph ▫$G$▫ by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. Minus graphs with game domination number equal to 3 are characterized. Double bluff graphs are also introduced and it is proved that Kneser graphs ▫$K(n,2)$▫, za ▫$n \ge 6$▫, are double bluff. The domination game is also studied on generalized Petersen graphs and on Hamming graphs. Several generalized Petersen graphs that are bluff graphs but not vertex-transitive are found. It is proved that Hamming graphs are not double bluff. |
|---|
| Keywords: | domination game, game domination number, bluff graphs, minus graphs, generalized Petersen graphs, Kneser graphs, Cartesian product of graphs, Hamming graphs |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Submitted for review: | 19.10.2015 |
|---|
| Article acceptance date: | 07.01.2016 |
|---|
| Publisher: | University of Zielona Góra |
|---|
| Year of publishing: | 2017 |
|---|
| Number of pages: | Str. 337-352 |
|---|
| Numbering: | Letn. 37, št. 2 |
|---|
| PID: | 20.500.12556/DKUM-65601  |
|---|
| ISSN: | 1234-3099 |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 1234-3099 |
|---|
| COBISS.SI-ID: | 17978457 |
|---|
| DOI: | 10.7151/dmgt.1899 |
|---|
| NUK URN: | URN:SI:UM:DK:DMQJPGXS |
|---|
| Publication date in DKUM: | 09.05.2017 |
|---|
| Views: | 1527 |
|---|
| Downloads: | 495 |
|---|
| Metadata: |    |
|---|
| Categories: | Misc.
|
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
