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arXiv · 2503.01310

An exact formula for the contraction factor of a subdivided Gaussian topological polymer

Jason Cantarella·Tetsuo Deguchi·Clayton Shonkwiler·Erica Uehara
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Abstract

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.

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Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, Erica Uehara. 2025-03-03. An exact formula for the contraction factor of a subdivided Gaussian topological polymer. https://doi.org/10.1088/1751--8121%2Fadfac3

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