on cycles in intersection graphs of rings

نویسندگان

n. ‎hoseini

department of pure mathematics, ferdowsi university of mashhad, mashhad, iran. a. erfanian

department of pure mathematics, ferdowsi university of mashhad, mashhad, iran. a. azimi

department of pure mathematics, ferdowsi university of mashhad, mashhad, iran. m. farrokhi d. g.

department of pure mathematics, ferdowsi university of mashhad, mashhad, iran.

چکیده

‎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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bulletin of the iranian mathematical society

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