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

• HONMA Hirotoshi
Department of Information Engineering, Kushiro National College of Technology
• ABE Kodai
Department of Intelligent Interaction Technologies, University of Tsukuba
• NAKAJIMA Yoko
Department of Information Engineering, Kushiro National College of Technology
• MASUYAMA Shigeru
Department of Computer Science and Engineering, Toyohashi University of Technology

## 抄録

Let Gs=(Vs,Es) be a simple connected graph. A vertex v ∈ Vs is an articulation vertex if deletion of v and its incident edges from Gs 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 ∈ Vs is called a hinge vertex if there exist any two vertices x and y in Gs 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.

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