On compressed zero divisor graphs associated to the ring of integers modulo $n$

Abstract

Let $R$ be a commutative ring with unity $1\ne 0$. In this paper, we completely describe the vertex and the edge chromatic number of the compressed zero divisor graph of the ring of integers modulo $n$. We find the clique number of the compressed zero divisor graph $\Gamma_E(\mathbb Z_n)$ of $\mathbb Z_n$ and show that $\Gamma_E(\mathbb Z_n)$ is weakly perfect. We also show that the edge chromatic number of $\Gamma_E(\mathbb Z_n)$ is equal to the largest degree proving that $\Gamma_E(\mathbb Z_n)$ resides in class 1 family of graphs.