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Exact solutions for the two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan

2006/12/30 by Christian Tanguy, Tanguy, Christian · 1 citation
Computer Science · Decision Sciences · Engineering · Mathematics · #FOS: Computer and information sciences #Graph theory and applications #Performance (cs.PF) #Probabilistic and Robust Engineering Design #Reliability and Maintenance Optimization #cs.PF

paper · pdf · doi:10.48550/arxiv.cs/0701005

arxiv created 2006/12/30 · openalex publication_date 2006/12/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The two- and all-terminal reliabilities of the Brecht-Colbourn ladder and the generalized fan have been calculated exactly for arbitrary size as well as arbitrary individual edge and node reliabilities, using transfer matrices of dimension four at most. While the all-terminal reliabilities of these graphs are identical, the special case of identical edge (p) and node (ρ) reliabilities shows that their two-terminal reliabilities are quite distinct, as demonstrated by their generating functions and the locations of the zeros of the reliability polynomials, which undergo structural transitions at ρ= 1/2.

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