Super Connectivity and Super Edge Connectivity of the Mycielskian of a Graph |
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Authors: | Litao Guo Ruifang Liu Xiaofeng Guo |
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Institution: | 1.School of Mathematical Sciences,Xiamen University,Xiamen,China;2.Department of Mathematics,Zhengzhou University,Zhengzhou,China |
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Abstract: | Mycielski introduced a new graph transformation μ(G) for graph G, which is called the Mycielskian of G. A graph G is super connected or simply super-κ (resp. super edge connected or super-λ), if every minimum vertex cut (resp. minimum edge cut) isolates a vertex of G. In this paper, we show that for a connected graph G with |V(G)| ≥ 2, μ(G) is super-κ if and only if δ(G) < 2κ(G), and μ(G) is super-λ if and only if
G\ncong K2{G\ncong K_2}. |
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