Volume 71 | Issue 7 | Year 2025 | Article Id. IJMTT-V71I7P109 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I7P109
Received | Revised | Accepted | Published |
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26 May 2025 | 30 Jun 2025 | 18 Jul 2025 | 28 Jul 2025 |
I. Rani, "Domination in Cubic Circulant Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 7, pp. 98-101, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I7P109
A Cayley graph is a graph constructed out of a group Γ and its generating set A. In this paper, the domination number of Cay(𝑍𝑛, A) = Cir(n, A), for the generating set A with cardinality three is determined.
Cayley graphs, Domination number, Dominating set, Gamma set.
[1] Teresa W. Haynes, Stephen Hedetniemi, and Peter Slater, Fundamentals of Domination in Graphs, CRC Press, 1998.
[CrossRef] [Google
Scholar] [Publisher Link]
[2] T. Tamizh Chelvam, and I. Rani, “Dominating Sets in Cayley graphs on Zn,” Tamkang Journal of Mathematics, vol. 38, no. 4, pp. 341
345, 2007.
[CrossRef] [Google Scholar] [Publisher Link]
[3] T. Tamizh Chelvam, and I. Rani, “Independent Domination Number of Cayley Graphs on Zn,” The Journal of Combinatorial and
Combinatorial Computing, vol. 69, pp. 251–255, 2009.
[Google Scholar] [Publisher Link]
[4] T. Tamizh Chelvam, and I. Rani, “Total and Connected Domination numbers for Cayley graphs on Zn,” Advanced Studies in Contemporary
Mathematics, vol. 20, no. 1, pp. 57-61, 2010.
[Google Scholar]
[5] S. Lakshmivarahan, and Sudarshan K. Dhall, “Rings, Torus and Hypercubes Architectures/ Algorithms for Parallel Computing,” Parallel
Computing, vol. 25, no. 13-14, pp. 1877-1906, 1999.
[CrossRef] [Google Scholar] [Publisher Link]
[6] Michael D. Plummer, “Some Recent Results on Domination in Graphs,” Discussiones Mathematicae Graph Theory, vol. 26, pp. 457-474,
2006.
[Google Scholar]
[7] Bruce Reed, “Paths, Stars, and The Number Three,” Combinatorics, Probability and Computing, vol. 5, no. 3, pp. 277-295, 1996.
[CrossRef] [Google Scholar] [Publisher Link]
[8] A.V. Kostochka, and B.Y. Stodolsky, “On Domination in Connected Cubic Graphs,” Discrete Mathematics, vol. 304, no. 1-3, pp. 45-50,
2005.
[CrossRef] [Google Scholar] [Publisher Link]
[9] Christian Löwenstein, and Dieter Rautenbach, “Domination in Graphs of Minimum Degree at Least Two and Large Girth,” Graphs and
Combinatorics, vol. 24, pp. 37–46, 2008.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Michael A. Henning, and Anders Yeo, Total Domination in Graphs, Springer Monographs in Mathematics, 2013. [CrossRef] [Google
Scholar] [Publisher Link]
[11] Paul Dorbec, and Michael Antony Henning, “The 1/3 - Conjectures for Domination in Cubic Graphs,” arXiv:2401.17820, 2024.
[CrossRef] [Google Scholar] [Publisher Link]
[12] Bin Sheng, and Changhong Lu, “The Paired Domination Number of Cubic Graphs,” arXiv preprint arXiv:2011.12496, 2020.
[CrossRef]
[Google Scholar] [Publisher Link]
[13] Simone Dantas et al., “Domination and Total Domination in Cubic Graphs of Large Girth,” Discrete Applied Mathematics, vol. 174, pp.
128–132, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
[14] Misa Nakanishi, “Generalized Domination Structure in Cubic Graphs,” arXiv:1901.10781, 2019.
[CrossRef] [Google Scholar] [Publisher
Link]