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On the connectedness of the complement of the zero-divisor graph of a poset. (English) Zbl 1420.05074
Summary: In this paper, connectedness is completely characterized for the complements of the zero-divisor graphs of partially ordered sets. These results are applied to annihilating ideal graphs and intersection graphs of submodules, generalizing some of the work that has recently appeared in the literature.

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