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On 3-restricted edge connectivity of undirected binary Kautz graphs |
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| Authors: | Jianping Ou Xiaohong Cheng |
| Institution: | a Institute of Applied Mathematics, Wuyi University, Jiangmen 529020, China b Library, Wuyi University, Jiangmen 529020, China c School of Mathematics and System Science, Shandong University, Jinan 250100, China |
| Abstract: | An edge cut of a connected graph is m-restricted if its removal leaves every component having order at least m. The size of minimum m-restricted edge cuts of a graph G is called its m-restricted edge connectivity. It is known that when m≤4, networks with maximal m-restricted edge connectivity are most locally reliable. The undirected binary Kautz graph UK(2,n) is proved to be maximal 2- and 3-restricted edge connected when n≥3 in this work. Furthermore, every minimum 2-restricted edge cut disconnects this graph into two components, one of which being an isolated edge. |
| Keywords: | Kautz graph Restricted edge connectivity |
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