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On the complement of the zero-divisor graph of a partially ordered set. (English) Zbl 1381.05030
Summary: In this paper, it is proved that the complement of the zero-divisor graph of a partially ordered set is weakly perfect if it has finite clique number, completely answering the question raised by V. Joshi and A. Khiste [Bull. Aust. Math. Soc. 89, No. 2, 177–190 (2014; Zbl 1288.05089)]. As a consequence, the intersection graph of an intersection-closed family of nonempty subsets of a set is weakly perfect if it has finite clique number. These results are applied to annihilating-ideal graphs and intersection graphs of submodules.

MSC:
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
06A07 Combinatorics of partially ordered sets
05C17 Perfect graphs
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