%0 Journal Article
%T On cycles in intersection graphs of rings
%J Bulletin of the Iranian Mathematical Society
%I Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Hoseini, N.
%A Erfanian, A.
%A Azimi, A.
%A Farrokhi D. G., M.
%D 2016
%\ 04/01/2016
%V 42
%N 2
%P 461-470
%! On cycles in intersection graphs of rings
%K Intersection graph
%K cycle
%K claw
%K Hamiltonian
%K pancyclic
%R
%X 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.
%U http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdf