Graph Theory With Applications
Graph Theory With Applications
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For a strongly connected digraph D=(V(D),A(D)), a vertex-cut S驴V(D) is a cyclic vertex-cut of D if D驴S has at least two strong components containing directed cycles. The cyclic vertex-connectivity 驴 c (D) is the minimum cardinality of all cyclic vertex-cuts of D.In this paper, we study 驴 c (D) for Cartesian product digraph D=D 1脳D 2, where D 1,D 2 are two strongly connected digraphs. We give an upper bound and a lower bound for 驴 c (D). Furthermore, the exact value of $\kappa_{c}(C_{n_{1}}\times C_{n_{2}}\times\cdots\times C_{n_{k}})$ is determined, where $C_{n_{i}}$ is the directed cycle of length n i for i=1,2,驴,k.