Bounds for the 2-Domination Number of Generalized Petersen Graphs P(ck,k)
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 numberReferences
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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.
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.
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Published
2022-09-20
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