Linear Time Algorithms for Finding Articulation and Hinge Vertices of Circular Permutation Graphs
Let G(s) = (V-s, E-s) be a simple connected graph. A vertex v is an element of 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 is an element of 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.
hinge vertices circular permutation graphs articulation vertices design and analysis of algorithms