On the Toughness of Some Generalized Petersen Graphs

Upper and lower bounds are established for the toughness of the generalized Petersen graphs \(G(n,2)\) for \(n \geq 5\), and all non-isomorphic disconnecting sets that achieve the toughness are presented for \(5 \leq n \leq 15\). These results also provide an infinite class of \(G(n,2)\) for which the toughness equals \(\frac{5}{4}\), namely when \(n \equiv 0 (\mod 7)\).