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Quaestiones Mathematicae

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On the connectedness of the complement of the zero-divisor graph of a poset

Sarika Devhare, Vinayak Joshi, John LaGrange

Abstract


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.

Key words: Zero-divisor graph, intersection graph, annihilating ideal graph, 0-distributive poset, 0-modular poset.




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