Degree-anonymization using edge rotations

The Min Anonymous-Edge-Rotation problem asks for an input graph G and a positive integer k to find minimum number of edge rotations that transform into such each vertex there are at least k−1 other vertices the same degree (a k-degree-anonymous graph). In this paper, we prove is NP-hard even k=n/q, where n order q any integer, q≥3. We argue under some constrains on edges in k, polynomial-time 2-approximable. Furthermore, show solvable polynomial time when k=n trees k=θ(n). Additionally, establish sufficient conditions solution exists.