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We use an algebraic method to classify the generalized permutation star-graphs, and we use the classification to determine the toughness of all generalized permutation star-graphs.
Motivated by the conjectures in [11], we introduce the maximal chains of a cycle permutation graph, and we use the properties of maximal chains to establish the upper bounds for the toughness of cycle permutation graphs. Our results confirm two conjectures in [11].
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