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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.01310 |
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| _version_ | 1866911196409495552 |
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| author | Cantarella, Jason Deguchi, Tetsuo Shonkwiler, Clayton Uehara, Erica |
| author_facet | Cantarella, Jason Deguchi, Tetsuo Shonkwiler, Clayton Uehara, Erica |
| contents | We consider the radius of gyration of a Gaussian topological polymer $G$ formed by subdividing a graph $G'$ of arbitrary topology (for instance, branched or multicyclic). We give a new exact formula for the expected radius of gyration and contraction factor of $G$ in terms of the number of subdivisions of each edge of $G'$ and a new weighted Kirchhoff index for $G'$. The formula explains and extends previous results for the contraction factor and Kirchhoff index of subdivided graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_01310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An exact formula for the contraction factor of a subdivided Gaussian topological polymer Cantarella, Jason Deguchi, Tetsuo Shonkwiler, Clayton Uehara, Erica Statistical Mechanics Combinatorics 82D60 (primary), 60G50, 60D05, 05C50 (secondary) We consider the radius of gyration of a Gaussian topological polymer $G$ formed by subdividing a graph $G'$ of arbitrary topology (for instance, branched or multicyclic). We give a new exact formula for the expected radius of gyration and contraction factor of $G$ in terms of the number of subdivisions of each edge of $G'$ and a new weighted Kirchhoff index for $G'$. The formula explains and extends previous results for the contraction factor and Kirchhoff index of subdivided graphs. |
| title | An exact formula for the contraction factor of a subdivided Gaussian topological polymer |
| topic | Statistical Mechanics Combinatorics 82D60 (primary), 60G50, 60D05, 05C50 (secondary) |
| url | https://arxiv.org/abs/2503.01310 |