On Eulerianity and Hamiltonicity in Annihilating-ideal Graphs

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.