Let R be a commutative ring with identity. For a positive integer n≥ 2, let M n (R) be the set
of all n× n matrices over R and M n (R)* be the set of all non-zero matrices of M n (R). The …

Let R be a commutative ring with identity, and let Z (R) be the set of zero-divisors of R. The
generalized zero-divisor graph of R is defined as the graph Γg (R) with the vertex set Z …

Let R be a commutative ring with identity and A (R) be the set of ideals with nonzero
annihilator. The strongly annihilating-ideal graph of R is defined as the graph SAG (R) with …

Let R be a commutative ring with identity and 𝔸 (R) be the set of ideals of R with nonzero
annihilator. The annihilator-ideal graph of R, denoted by AI (R), is a simple graph with the …

Let R be a commutative ring with identity. The co-maximal ideal graph of R, denoted by Γ
(R), is a simple graph whose vertices are proper ideals of R which are not contained in the …

Let F q be a finite field with q elements, R 0= M n (F q) be the ring of all n× n matrices over F
q, L (R 0) be the set of all nontrivial left ideals of R 0. The co-maximal ideal graph of R 0 …

Let R be a commutative ring with identity 1≠ 0. The comaximal ideal graph of R is the
simple, undirected graph whose vertex set is the set of all proper ideals of the ring R not …

ON THE PLANARITY AND PERFECTNESS OF ANNIHILATOR IDEAL GRAPHS Page 1
TAMKANG JOURNAL OF MATHEMATICS Volume 50, Number 4, 361-369, December 2019 …