TY - JOUR ID - 772 TI - On cycles in intersection graphs of rings JO - Bulletin of the Iranian Mathematical Society JA - BIMS LA - en SN - 1017-060X AU - ‎Hoseini, N. AU - Erfanian, A. AU - Azimi, A. AU - Farrokhi D. G., M. AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran. Y1 - 2016 PY - 2016 VL - 42 IS - 2 SP - 461 EP - 470 KW - Intersection graph‎ KW - ‎cycle‎ KW - ‎claw‎ KW - ‎Hamiltonian‎ KW - ‎pancyclic DO - N2 - ‎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. UR - http://bims.iranjournals.ir/article_772.html L1 - http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdf ER -