On super 2-restricted and 3-restricted edge-connected vertex transitive graphs |
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Authors: | Weihua Yang Zhao Zhang Chengfu Qin Xiaofeng Guo |
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Institution: | 1. School of Mathematical Science, Xiamen University, Xiamen Fujian 361005, China;2. College of Mathematics and Systems Sciences, Xinjiang University, Urumqi 830046, China |
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Abstract: | Let be a simple connected graph and . An edge set is an -restricted edge cut if is disconnected and each component of contains at least vertices. Let be the minimum size of all -restricted edge cuts and , where is the set of edges with exactly one end vertex in and is the subgraph of induced by . A graph is optimal- if . An optimal- graph is called super -restricted edge-connected if every minimum -restricted edge cut is for some vertex set with and being connected. In this note, we give a characterization of super 2-restricted edge-connected vertex transitive graphs and obtain a sharp sufficient condition for an optimal- vertex transitive graph to be super 3-restricted edge-connected. In particular, a complete characterization for an optimal- minimal Cayley graph to be super 2-restricted edge-connected is obtained. |
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