A graph is well-(edge-)dominated if every minimal (edge) dominating set is minimum. A graph is equimatchable if every maximal matching is maximum. We study these concepts on strong product graphs. We fully characterize well-edge-dominated and equimatchable strong product graphs of nontrivial graphs, and identify a large family of graphs whose strong products with any well-dominated graph are well-dominated.
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Cao et al. (2024) studied this question.
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