| Title: | More results on the domination number of Cartesian product of two directed cycles |
|---|
| Authors: | ID Ye, Ansheng (Author)
ID Miao, Fang (Author)
ID Shao, Zehui (Author)
ID Liu, Jia-Bao (Author)
ID Žerovnik, Janez (Author)
ID Repolusk, Polona (Author) |
|---|
| Files: |  http://dx.doi.org/10.3390/math7020210
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FNM - Faculty of Natural Sciences and Mathematics
|
|---|
| Abstract: | Let γ(D) denote the domination number of a digraph D and let C$_m$□C$_n$ denote the Cartesian product of C$_m$ and C$_n$, the directed cycles of length n ≥ m ≥ 3. Liu et al. obtained the exact values of γ(C$_m$□C$_n$) for m up to 6 [Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36–39]. Shao et al. determined the exact values of γ(C$_m$□C$_n$) for m = 6, 7 [On the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 619695]. Mollard obtained the exact values of γ(C$_m$□C$_n$) for m = 3k + 2 [M. Mollard, On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths, Discuss. Math. Graph Theory 33(2) (2013) 387–394.]. In this paper, we extend the current known results on C$_m$□C$_n$ with m up to 21. Moreover, the exact values of γ(C$_n$□C$_n$) with n up to 31 are determined. |
|---|
| Keywords: | domination number, Cartesian product, directed cycle |
|---|
| Year of publishing: | 2019 |
|---|
| Number of pages: | Str. 1-9 |
|---|
| Numbering: | ǂVol. ǂ7, ǂno. ǂ2 |
|---|
| PID: | 20.500.12556/DKUM-80902  |
|---|
| UDC: | 519.1 |
|---|
| ISSN on article: | 2227-7390 |
|---|
| COBISS.SI-ID: | 24462088 |
|---|
| DOI: | 10.3390/math7020210 |
|---|
| Publication date in DKUM: | 02.09.2022 |
|---|
| Views: | 800 |
|---|
| Downloads: | 16 |
|---|
| 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. |
