The clique number of the intersection graph of some cyclic groups

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics, University of Zanjan, P.O. Box 45371-38791, Zanjan, Iran

Abstract

For a nontrivial finite group $G$, the intersection graph $\Gamma(G)$ of $G$ is a simple undirected graph whose vertices are the nontrivial proper subgroups of $G$ and two vertices are joined by an edge if and only if they have a nontrivial intersection. In this paper, we obtain the clique number of the intersection graph of cyclic groups whose orders have four prime divisors. Moreover we find the clique number of the intersection graph of cyclic groups of order $n$ such that all powers of prime divisors of $n$ are equal. As a special case, we find the clique number of this graph for the cyclic groups of the square-free orders.

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References

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International Journal of Group Theory

Articles in Press, Corrected Proof
Available Online from 11 March 2025

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History

  • Receive Date: 17 February 2024
  • Revise Date: 10 March 2025
  • Accept Date: 11 March 2025
  • Published Online: 11 March 2025

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