Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X42220160401On cycles in intersection graphs of rings461470772ENN.HoseiniDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.A.ErfanianDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.A.AzimiDepartment of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.M.Farrokhi D. G.Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.Journal Article20131105Let $R$ 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.http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdf