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I'm unsure if this satisfies the definition of vertex cover, the graph is unweighted and undirected:

enter image description here

if not, an explanation would be super enlighting.

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    $\begingroup$ What definition were you given ? $\endgroup$
    – user16034
    Commented Jul 29, 2023 at 19:42

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Yes, this is a vertex cover (VC).

By definition, a vertex cover of a graph G=(V,E) is a subset of nodes $U\subset V$ such that $\forall \ e \in E \ \exists u \in U$ such that $e$ is incident in $u$.

Every edge in your graph has one of its extremes in the VC, so yes

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