Let G be a graph. Then T in contained in V(G) is called an R~2-vertex-cut if G - T is disconnected and each vertex in V(G) - T has at least two neighbors in G - T. The size of a smallest R~2-vertex-cut is the R~2 -vertex-connectivity of G and is denoted by k~2(G). In this paper, we determine this number for Cayley graphs generated by transposition trees.
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