TY - JOUR
T1 - Reliability Polynomials and Their Asymptotic Limits for Families of Graphs
AU - Chang, Shu Chiuan
AU - Shrock, Robert
N1 - Funding Information:
This research was partially supported by the NSF Grant PHY-00-98527.
PY - 2003/9
Y1 - 2003/9
N2 - 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.
AB - 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.
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U2 - 10.1023/A:1024663508526
DO - 10.1023/A:1024663508526
M3 - Article
AN - SCOPUS:0038167277
VL - 112
SP - 1019
EP - 1077
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 5-6
ER -