A linear time algorithm for finding all hinge vertices of a permutation graph

If the distance of any two vertices becomes longer after a vertex u is removed, then u is called a hinge vertex. The fault of a hinge vertex will increase the overall communication cost in a network. Therefore, finding the set of all hinge vertices in a graph can be used to identify critical nodes in a real network. We shall propose a linear time algorithm for finding all hinge vertices of a permutation graph.