Eulerian and pancyclic zero-divisor graphs of ordered sets

Abstract

In this paper, we determine when the zero-divisor graph of a special class of a finite pseudocomplemented poset is Eulerian. Also, we deal with Hamiltonian, vertex pancyclic, and edge pancyclic properties of the complement of a zero-divisor graph of finite 0-distributive posets. These results are applied to study the Eulerian, Hamiltonian and pancyclic properties of the zero-divisor graph, comaximal ideal graph, annihilating ideal graph, intersection ideal graph of a special class of commutative rings and intersection graph of a special class of groups.

Keywords

• 05C15
• 06A07
• 13A70
• Eulerian graph
• Hamiltonian graph
• zero-divisor graphs