| Title: | Domination game critical graphs |
|---|
| Authors: | ID Bujtás, Csilla (Author)
ID Klavžar, Sandi (Author)
ID Košmrlj, Gašper (Author) |
|---|
| Files: |  Discussiones_Mathematicae_Graph_Theory_2015_Bujtas,_Klavzar,_Kosmrlj_Domination_game_critical_graphs.pdf (194,74 KB)
MD5: F52741DC9E1C4954DB3E246A85FD7EC7
 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1839
|
|---|
| 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 a graph ▫$G$▫ by two players who alternately take turns by choosing a vertex such that in each turn at least one previously undominated vertex is dominated. The game is over when each vertex becomes dominated. One of the players, namely Dominator, wants to finish the game as soon as possible, while the other one wants to delay the end. The number of turns when Dominator starts the game on ▫$G$▫ and both players play optimally is the graph invariant ▫$\gamma_g(G)$▫, named the game domination number. Here we study the ▫$\gamma_g$▫-critical graphs which are critical with respect to vertex predomination. Besides proving some general properties, we characterize ▫$\gamma_g$▫-critical graphs with ▫$\gamma_g =2$▫ and with ▫$\gamma_g =3$▫, moreover for each ▫$n$▫ we identify the (infinite) class of all ▫$\gamma_g$▫-critical ones among the ▫$n$▫th powers ▫$C_N^n$▫ of cycles. Along the way we determine ▫$\gamma_g(C_N^n)$▫ for all ▫$n$▫ and ▫$N$▫. Results of a computer search for ▫$\gamma_g$▫-critical trees are presented and several problems and research directions are also listed. |
|---|
| Keywords: | domination game, domination game critical graphs, powers of cycles, trees |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Submitted for review: | 31.08.2024 |
|---|
| Article acceptance date: | 20.02.2025 |
|---|
| Publication date: | 28.02.2025 |
|---|
| Number of pages: | str. 781-796 |
|---|
| Numbering: | Letn. 35, št. 4 |
|---|
| PID: | 20.500.12556/DKUM-65335  |
|---|
| ISSN: | 1234-3099 |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 1234-3099 |
|---|
| COBISS.SI-ID: | 17464921 |
|---|
| NUK URN: | URN:SI:UM:DK:D0MNDQWR |
|---|
| Publication date in DKUM: | 31.03.2017 |
|---|
| Views: | 1400 |
|---|
| Downloads: | 438 |
|---|
| 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. |
