Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models
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) = Sigma(G'subset o...
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2002
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| Online Access: | http://shdl.mmu.edu.my/2646/ |
| _version_ | 1848790113463566336 |
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| author | Bhatti, Faqir M Abu, Nur Azman |
| author_facet | Bhatti, Faqir M Abu, Nur Azman |
| author_sort | Bhatti, Faqir M |
| building | MMU Institutional Repository |
| collection | Online Access |
| description | 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) = Sigma(G'subset of or equal toG)(-1)(e-e') F(G')eta(G'), where eta(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. |
| first_indexed | 2025-11-14T18:07:27Z |
| format | Article |
| id | mmu-2646 |
| institution | Multimedia University |
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| last_indexed | 2025-11-14T18:07:27Z |
| publishDate | 2002 |
| recordtype | eprints |
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| spelling | mmu-26462011-09-08T03:26:51Z http://shdl.mmu.edu.my/2646/ Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models Bhatti, Faqir M Abu, Nur Azman QC Physics 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) = Sigma(G'subset of or equal toG)(-1)(e-e') F(G')eta(G'), where eta(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. 2002-01 Article NonPeerReviewed Bhatti, Faqir M and Abu, Nur Azman (2002) Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models. Journal of the Physical Society of Japan, 71 (1). pp. 43-48. ISSN 00319015 http://dx.doi.org/10.1143/JPSJ.71.43 doi:10.1143/JPSJ.71.43 doi:10.1143/JPSJ.71.43 |
| spellingShingle | QC Physics Bhatti, Faqir M Abu, Nur Azman Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models |
| title | Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models |
| title_full | Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models |
| title_fullStr | Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models |
| title_full_unstemmed | Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models |
| title_short | Some Properties of Weight Factors arising in Low-Density Series Expansion for Percolation Models |
| title_sort | some properties of weight factors arising in low-density series expansion for percolation models |
| topic | QC Physics |
| url | http://shdl.mmu.edu.my/2646/ http://shdl.mmu.edu.my/2646/ http://shdl.mmu.edu.my/2646/ |