Vishnu B. Tanpure

Zero divisors of Gorenstein Rings

Let $R$ be a commutative Artinian ring. We consider two graphs associated to $R$, namely the compressed zero-divisor graph $\Gamma_E(R)$ and the associate class graph $\Gamma_A(R)$. Partitioning the vertex set of a zero-divisor graph into its core and its boundary, we count the core vertices that dominate the core. Thi...