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.
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