Bulletin of the Iranian Mathematical Society, Volume (42), No (2), Year (2016-5) , Pages (461-470)

Title : ( ON Cycles IN Intersection Graghs OF Rings )

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

Let R be a commutative ring with non-zero identity. We describe all C3- and C4-free intersection graphs of non-trivial ideals of R as well as Cn-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

, Intersection graph, cycle, claw, Hamiltonian, pancyclic