Cohen–macauleyness of the Zero-Divisor Graph of a Boolean Poset

Key Points

• The aim is to establish that the zero-divisor graph of a Boolean poset is both well-covered and Cohen–Macaulay.
• Proved properties of zero-divisor graphs for Boolean posets.
• Analyzed the structure of posets as products of single bounded posets.
• Determined the conditions under which the zero-divisor graph is Cohen–Macaulay.
• The zero-divisor graph of any Boolean poset is well-covered and Cohen–Macaulay.
• For the poset product, the zero-divisor graph is Cohen–Macaulay if and only if the product is a Boolean lattice.