科研之友
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摘要
Mycielski introduced a new graph transformation mu(G) for graph G, which is called the Mycielskian of G. A graph G is super connected or simply super-kappa (resp. super edge connected or super-lambda), 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, mu(G) is super-kappa if and only if delta(G) < 2 kappa(G), and mu(G) is super-lambda if and only if delta(G) < 2 kappa(G), and mu(G) is super-lambda if and only if G not congruent to K-2.
