For squarefree n = p1 p2 ... pm, the vertex connectivity of the nonzero nonunit core G2 of the comaximal graph Γ(Z_n) is exactly ∏_{i=1}^{m-1} (p_i - 1) = φ(n) / (p_m - 1).
Mohar, The Laplacian spectrum of graphs, inGraph Theory, Combinatorics, and Applications, Vol
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Vertex connectivity of the nonzero nonunit core of the comaximal graph of $\mathbb Z_n$
For squarefree n = p1 p2 ... pm, the vertex connectivity of the nonzero nonunit core G2 of the comaximal graph Γ(Z_n) is exactly ∏_{i=1}^{m-1} (p_i - 1) = φ(n) / (p_m - 1).