Reliability Polynomials and Their Asymptotic Limits for Families of Graphs

Shu Chiuan Chang, Robert Shrock

研究成果: Article同行評審

19 引文 斯高帕斯(Scopus)

摘要

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.

原文English
頁(從 - 到)1019-1077
頁數59
期刊Journal of Statistical Physics
112
發行號5-6
DOIs
出版狀態Published - 2003 九月

All Science Journal Classification (ASJC) codes

  • 統計與非線性物理學
  • 數學物理學

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