Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models

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概要

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• Let F(G) be any additive property of a simple graph such that F(G)=F(G_1)+F(G_2), where G is the series combination of graphs G_1 and G_2. The weight factor W(G) which is based on F(G) arises in the low-density series expansion techniques for percolation models as W(G)Σ_<G'⊊︀G(-1)^<e-e'F(G')η(G'), where η(G') is the indicator that G' cover-able sub-graph or without dangling ends. The purpose of this paper is to prove the weight factor formula for additive property of F as W(G)=d(G_2)W(G_1)+d(G_1)W(G_2), where d(G_1) are d(G_2) the d-weight for graphs G_1 and G_2 respectively. This result will be more simplified in the case of Directed Percolation Models using Mobius function property. A new few formulas for the resistive weight factors are also derived for a graph, which is parallel combination of n edges.

• 社団法人日本物理学会の論文
• 2002-01-15

著者

• Bhatti Faqir

  Faculty Of Information Science And Technology Multimedia University

• ABU Nur

  Faculty of Information Science and Technology, Multimedia University

• Abu Nur

  Faculty Of Information Science And Technology Multimedia University

関連論文

• Low-Density Series Expansion for the Domany-Kinzel Model : General Physics
• Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models

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