Reliability Polynomials and Their Asymptotic Limits for Families of Graphs

Shu Chiuan Chang, Robert Shrock

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

We present exact calculations of reliability polynomials R(G, p) for lattice strips G of fixed widths L y ≤ 4 and arbitrarily great length L x with various boundary conditions. We introduce the notion of a reliability per vertex, r({G}, p) = lim |v| → ∞ R(G, p) 1|V| where |V| denotes the number of vertices in G and {G} denotes the formal limit lim |V| → ∞ G. We calculate this exactly for various families of graphs. We also study the zeros of R(G, p) in the complex p plane and determine exactly the asymptotic accumulation set of these zeros ℬ across which r({G}) is nonanalytic.

Original languageEnglish
Pages (from-to)1019-1077
Number of pages59
JournalJournal of Statistical Physics
Volume112
Issue number5-6
DOIs
Publication statusPublished - 2003 Sep 1

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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