ojs2 has produced an error Message: WARNING: mkdir(): Permission denied In file: /var/www/html/ojs246_old/lib/pkp/classes/file/FileManager.inc.php At line: 306 Stacktrace: Server info: OS: Linux PHP Version: 5.6.33-0+deb8u1 Apache Version: Apache/2.4.10 (Debian) DB Driver: mysql DB server version: 5.7.27
ojs2 has produced an error Message: WARNING: assert(): Assertion failed In file: /var/www/html/ojs246_old/plugins/generic/usageStats/UsageStatsPlugin.inc.php At line: 308 Stacktrace: Server info: OS: Linux PHP Version: 5.6.33-0+deb8u1 Apache Version: Apache/2.4.10 (Debian) DB Driver: mysql DB server version: 5.7.27
Bounds for the 2-Domination Number of Generalized Petersen Graphs P(ck,k) | Chaiya | งดใช้ระบบ 3-31 กค 66 Burapha Science Journal

Bounds for the 2-Domination Number of Generalized Petersen Graphs P(ck,k)

Yanisa Chaiya, Jitsupa Srisawat, Natnicha Thanomngam, Nattawadee Butthaworn

Abstract


Let  G=(V,E) be a graph. A subset D of G is a 2-dominating set of G if each vertex in V-D is adjacent to at least 2 vertices in D. The 2-domination number of  is the cardinality of the smallest 2-dominating set of G. In this paper, we give a lower and upper bound on the 2-domination number of generalized Petersen graphs P(ck,k), where c and k are integers in which c>2.

Keywords :  generalized Petersen graphs; 2-dominating sets; 2-domination number


Full Text:

PDF

References


Arash, B., Mehdi, B. & Elisabeth P.C. (2008). On the domination number of generalized Petersen Graphs. Discrete Math., 308, 603-610.

Bakhshesh, D., Farshi, M. & Hooshmandasl, M.R. (2018). 2-domination number of generalized Petersen graphs. Proc. Indian Acad. Sci. (Math. Sci.), 128, Article ID : 0017

Chen, X. & Zhao, X. (2020). The exact 2-domination number of generalized Petersen graphs. Proc. Indian Acad.Sci. (Math.Sci), 130, 1-6.

Cheng, Y. (2013). α-domination of generalized Petersen graphs, Ph.D. thesis (National Chiao Tung University).

Ebrahimi, B.J., Jahanbakht, N. & Mahmoodian, E.S. (2009). Vertex domination of generalized Petersen graphs. Discrete Math., 309, 4355-4361.

Fu, X., Yang, Y. & Jiang, B. (2009). On the domination number of generalized Petersen graphs P(n,2). Discrete Math., 309, 2445-2451.

Yang, H., Kang, L., & Xu, G. (2009). The exact domination number of generalized Petersen graphs. Discrete Math., 309, 2596-2607.

Zhao, W., Zheng, M., & Wu, L. (2010). Domination Number of Generalized Petersen graphs P(ck,k). Util. Math., 81, 157-163.


Refbacks

  • There are currently no refbacks.