TY - JOUR
T1 - On Eulerianity and Hamiltonicity in Annihilating-ideal Graphs
TT -
JF - IJMSI
JO - IJMSI
VL - 16
IS - 1
UR - http://ijmsi.ir/article-1-1251-en.html
Y1 - 2021
SP - 97
EP - 104
KW - Annihilating-ideal graph
KW - Eulerian graphs
KW - Hamiltonian graphs
N2 - Let $R$ be a commutative ring with identity, and $ mathrm{A}(R) $ be the set of ideals with non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $AG(R)$ with the vertex set $ mathrm{A}(R)^{*}=mathrm{A}(R)setminuslbrace 0rbrace $ and two distinct vertices $ I $ and $ J $ are adjacent if and only if $ IJ=0 $. In this paper, conditions under which $AG(R)$ is either Eulerian or Hamiltonian are given.
M3
ER -