On co-maximal subgroup graph of $Z_n$

Document Type : Research Paper

Authors

Department of Mathematics, Presidency University, Kolkata

Abstract

The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is a graph whose vertices are non-trivial proper subgroups of $G$ and two vertices $H$ and $K$ are adjacent if $HK = G$‎. ‎In this paper‎, ‎we study and characterize various properties like diameter‎, ‎domination number‎, ‎perfectness‎, ‎hamiltonicity‎, ‎etc‎. ‎of $\Gamma(\mathbb{Z}_n)$

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References

[1] S. Akbari, B. Miraftab and R. Nikandish, Co-maximal Graphs of Subgroups of Groups, Canad. Math. Bull., 60 (2017) 12–25.
[2] P. J. Cameron, Graphs defined on groups, Int. J. Group Theory, Article in Press. https://ijgt.ui.ac.ir/article_25608.html.
[3] A. Das, M. Saha and S. Alkaseasbeh, On Co-Maximal Subgroup Graph of a Group, https://arxiv.org/pdf/2103.14284.pdf
[4] B. Miraftab and R. Nikandish, Co-maximal Graphs of Two Generator Groups, J. Algebra Appl., 18 (2019) pp. 13.
International Journal of Group Theory
Volume 11, Issue 4 - Serial Number 4
December 2022
Pages 221-228

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History

  • Receive Date: 06 August 2021
  • Revise Date: 27 September 2021
  • Accept Date: 29 September 2021
  • Published Online: 01 December 2022

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