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Eulerian and Hamiltonian complements of zero-divisor graphs of pseudocomplemented posets. (English) Zbl 1441.05130
Summary: In this paper, Eulerian complements of zero-divisor graphs are classified for a special class of finite pseudocomplemented posets. Also, it is proved that the complement of the zero-divisor graph of a finite pseudocomplemented poset \(P\) is Hamiltonian if and only if \(P\) has at least three atoms. These results are applied to zero-divisor graphs and intersection graphs of ideals of reduced commutative Artinian rings.
MSC:
05C45 Eulerian and Hamiltonian graphs
13A70 General commutative ring theory and combinatorics (zero-divisor graphs, annihilating-ideal graphs, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
06A07 Combinatorics of partially ordered sets
13A05 Divisibility and factorizations in commutative rings
13E10 Commutative Artinian rings and modules, finite-dimensional algebras
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