Celino Miguel
Abstract
LetR be a finite commutative ring with identity. We prove that if R is a principal ideal ring then the directed zero-divisor graph Γ(M n (R)) is balanced and eulerian. We also find the smallest finite commutative ring R with identity such that Γ(M n (R)) is not balanced.
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LetR be a finite commutative ring with identity. We prove that if R is a principal ideal ring then the directed zero-divisor graph Γ(M n (R)) is balanced and eulerian. We also find the smallest finite commutative ring R with identity such that Γ(M n (R)) is not balanced.
Key concepts: Mathematics, Zero divisor, Commutative ring, Principal ideal, Principal ideal ring, Combinatorics, Zero (linguistics), Reduced ring