Linear Time Algorithms for Finding Articulation and Hinge Vertices of Circular Permutation Graphs

Abstract

Let G_s=(V_s,E_s) be a simple connected graph. A vertex v ∈ V_s is an articulation vertex if deletion of v and its incident edges from G_s disconnects the graph into at least two connected components. Finding all articulation vertices of a given graph is called the articulation vertex problem. A vertex u ∈ V_s is called a hinge vertex if there exist any two vertices x and y in G_s whose distance increase when u is removed. Finding all hinge vertices of a given graph is called the hinge vertex problem. These problems can be applied to improve the stability and robustness of communication network systems. In this paper, we propose linear time algorithms for the articulation vertex problem and the hinge vertex problem of circular permutation graphs.