The super-connected property of recursive circulant graphs

Authors:
Chang-Hsiung Tsai;Jimmy J. M. Tan;Lih-Hsing Hsu
Affiliations:
Department of Computer Science and Information Engineering, Dahan Institute of Technology, Hualien 971, Taiwan, ROC;Department of Computer and Information Science, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Information Engineering, Ta Hwa Institute of Technology, Hsinchu 307, Taiwan, ROC
Venue:
Information Processing Letters
Year:
2004

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Abstract

In a graph G, a k-container Ck(u, v) is a set of k disjoint paths joining u and v. A k-container Ck(u, v) is k*-container if every vertex of G is passed by some path in Ck(u, v). A graph G is k*-connected if there exists a k*-container between any two vertices. An m-regular graph G is super-connected if G is k*-connected for any k with 1 ≤ k ≤ m. In this paper, we prove that the recursive circulant graphs G(2m, 4), proposed by Park and Chwa [Theoret. Comput. Sci. 244 (2000) 35-62], are super-connected if and only if m ≠ 2.