# On cycles in intersection graphs of rings

Document Type: Research Paper

Authors

Abstract

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ‎We show that such graphs are indeed pancyclic.

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### History

• Receive Date: 05 November 2013
• Revise Date: 14 February 2015
• Accept Date: 15 February 2015