Document Type: Research Paper

**Authors**

Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.

**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.

**Keywords**

**Main Subjects**

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Volume 42, Issue 2

March and April 2016

Pages 461-470

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