TY - JOUR
ID - 772
TI - On cycles in intersection graphs of rings
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Hoseini, N.
AU - Erfanian, A.
AU - Azimi, A.
AU - Farrokhi D. G., M.
AD - Department of Pure Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.
Y1 - 2016
PY - 2016
VL - 42
IS - 2
SP - 461
EP - 470
KW - Intersection graph
KW - cycle
KW - claw
KW - Hamiltonian
KW - pancyclic
DO -
N2 - 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.
UR - http://bims.iranjournals.ir/article_772.html
L1 - http://bims.iranjournals.ir/article_772_474628f752047d413e00702e57860add.pdf
ER -