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A subset F⊂V(G) is called an R2-vertex-cut of G if G−F is disconnected and each vertex u∈V(G)−F has at least two neighbors in G−F. The cardinality of a minimum R2-vertex-cut of G, denoted by κ2(G), is the R2-vertex-connectivity of G. In this work, we prove that κ2(Sn)=6(n−3) for n≥4, where Sn is the n-dimensional star graph.
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