Analysis identifies NP-completeness in determining double domination number for bipartite graphs, suggesting complexity in tree structures.
In this paper, we study on double domination ([Formula: see text]) and double edge-vertex domination ([Formula: see text]) of trees. We obtain that determining the double [Formula: see text]-domination number is NP-complete for bipartite graphs. We also obtain that [Formula: see text] for a tree [Formula: see text] and as an implementation, we present the family of trees achieving the equality [Formula: see text].
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Şahin et al. (2025) studied this question.
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