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Super-Connectivity and Hyper-Connectivity of Vertex Transitive Bipartite Graphs

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Abstract

A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if the deletion of each minimum vertex cut creates exactly two components, one of which is an isolated vertex. In this note, we proved that a vertex transitive bipartite graph is not super-connected if and only if it is isomorphic to the lexicographic product of a cycle C n (n ≥  6) by a null graph N m . We also characterized non-hyper-connected vertex transitive bipartite graphs.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, People’s Republic of China

    Xiaodong Liang, Jixiang Meng & Zhao Zhang

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  1. Xiaodong Liang
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  2. Jixiang Meng
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  3. Zhao Zhang
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Correspondence to Xiaodong Liang.

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Liang, X., Meng, J. & Zhang, Z. Super-Connectivity and Hyper-Connectivity of Vertex Transitive Bipartite Graphs. Graphs and Combinatorics 23, 309–314 (2007). https://doi.org/10.1007/s00373-007-0725-0

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  • DOI: https://doi.org/10.1007/s00373-007-0725-0

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