On cyclic vertex-connectivity of Cartesian product digraphs

Da Huang and Zhao Zhang ()
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Da Huang: Xinjiang University
Zhao Zhang: Xinjiang University

Journal of Combinatorial Optimization, 2012, vol. 24, issue 3, No 16, 379-388

Abstract: Abstract For a strongly connected digraph D=(V(D),A(D)), a vertex-cut S⊆V(D) is a cyclic vertex-cut of D if D−S has at least two strong components containing directed cycles. The cyclic vertex-connectivity κ c (D) is the minimum cardinality of all cyclic vertex-cuts of D. In this paper, we study κ c (D) for Cartesian product digraph D=D 1×D 2, where D 1,D 2 are two strongly connected digraphs. We give an upper bound and a lower bound for κ 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,…,k.

Keywords: Cartesian product digraph; Cyclic vertex-connectivity (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10878-011-9395-1

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