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 \({G\ncong K_2}\).
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Guo, L., Liu, R. & Guo, X. Super Connectivity and Super Edge Connectivity of the Mycielskian of a Graph. Graphs and Combinatorics 28, 143–147 (2012). https://doi.org/10.1007/s00373-011-1032-3
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DOI: https://doi.org/10.1007/s00373-011-1032-3