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arXiv · 1401.6619

On cycles in intersection graph of rings

Ali Azimi·Ahmad Erfanian·Mohammad Farrokhi Derakhshandeh Ghouchan·Nesa Hoseini
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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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Ali Azimi, Ahmad Erfanian, Mohammad Farrokhi Derakhshandeh Ghouchan, Nesa Hoseini. 2014-01-26. On cycles in intersection graph of rings. https://arxiv.org/abs/1401.6619

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