On cycles in intersection graph of rings

Ali Azimi; Ahmad Erfanian; Mohammad Farrokhi Derakhshandeh Ghouchan; Nesa Hoseini

On cycles in intersection graph of rings

Commutative Algebra 2014-01-28 v1

Authors: Ali Azimi , Ahmad Erfanian , Mohammad Farrokhi Derakhshandeh Ghouchan , Nesa Hoseini

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.

Keywords

zero-divisor graphs hamilton cycles intersection theory

Cite

@article{arxiv.1401.6619,
  title  = {On cycles in intersection graph of rings},
  author = {Ali Azimi and Ahmad Erfanian and Mohammad Farrokhi Derakhshandeh Ghouchan and Nesa Hoseini},
  journal= {arXiv preprint arXiv:1401.6619},
  year   = {2014}
}

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8 pages, 6 figures

On cycles in intersection graph of rings

Abstract

Keywords

Cite

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