Graph theoretic reliability analysis for the Boolean n cube networks

Yang, Chu-Sing; Wang, J.F.; Lee, J.Y.; Boesch, Francis T.

doi:10.1109/31.7582

Cited by 36 publications

(20 citation statements)

References 16 publications

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“…It has been shown that a super-λ network is the most reliable and has the smallest edge failure rate (see, e.g., [17,18]). Several sufficient conditions for a graph to be max-λ or super-λ have been given in the literature (see, e.g., [6]).…”

Section: It Is Well Known That λ(G) ≤ δ(G) Where δ(G) Is the Minimummentioning

confidence: 99%

On super edge‐connectivity of Cartesian product graphs

Lü

Chen

2006

Networks

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The super edge-connectivity λ of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G − F contains at least two vertices. Let G i be a connected graph with order n i , minimum degree δ i and edge-connectivity λ i for i = 1, 2. This article shows that λ (G 1 × G 2 ) ≥ min{n 1 λ 2 , n 2 λ 1 , λ 1 + 2λ 2 , 2λ 1 +λ 2 } for n 1 , n 2 ≥ 3 and λ (K 2 ×G 2 ) = min{n 2 , 2λ 2 }, which generalizes the main result of Shieh on the super edge-connectedness of the Cartesian product of two regular graphs with maximum edge-connectivity. In particular, this article determines λ (G 1 × G 2 ) = min{n 1 δ 2 , n 2 δ 1 , ξ(G 1 × G 2 )} if λ (G i ) = ξ(G i ), where ξ(G) is the minimum edge-degree of a graph G.

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Section: It Is Well Known That λ(G) ≤ δ(G) Where δ(G) Is the Minimummentioning

confidence: 99%

On super edge‐connectivity of Cartesian product graphs

Lü

Chen

2006

Networks

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“…It has been shown that a super connected network is most reliable and has the smallest vertex failure rate among all the networks with the same connectivity (see, for example, [20,21]). …”

Section: It Is Well Known That κ(G) ≤ δ(G) a Graph G Is Said To Be Mmentioning

confidence: 99%

On super connectivity of Cartesian product graphs

Lü

Chen

et al. 2008

Networks

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The super connectivity κ 1 of a connected graph G is the minimum number of vertices whose deletion results in a disconnected graph without isolated vertices; this is a more refined index than the connectivity parameter κ. This article provides bounds for the super connectivity κ 1 of the Cartesian product of two connected graphs, and thus generalizes the main result of Shieh on the super connectedness of the Cartesian product of two regular graphs with maximum connectivity. Particularly, we determine that κ 1 (K m × K n ) = min{m + 2n − 4, 2m + n − 4} for m + n ≥ 6 and state sufficient conditions to guarantee κ 1 (K 2 × G) = 2κ(G). As a consequence, we immediately obtain the super connectivity of the n-cube for n ≥ 3.

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“…Formula (2) demonstrates the relationship between two extremal problems: finding t-optimal and maximally reliable graphs. Approximation (2) is good for highly unreliable networks, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Let us assume that failures of lines are statistically independent with the same probability of failure 1 À p. Probability that a network is connected is given by the reliability polynomial [1,2]:…”

Section: Introductionmentioning

confidence: 99%