on cycles in intersection graphs of rings
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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.
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Journal title:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۲، صفحات ۴۶۱-۴۷۰
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