on cycles in intersection graphs of rings
نویسندگان
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.
منابع مشابه
On cycles in intersection graphs of rings
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. ...
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عنوان ژورنال:
bulletin of the iranian mathematical societyجلد ۴۲، شماره ۲، صفحات ۴۶۱-۴۷۰
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