English

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

Statistical Mechanics 2025-10-09 v1 Combinatorics

Abstract

We consider the radius of gyration of a Gaussian topological polymer GG formed by subdividing a graph GG' of arbitrary topology (for instance, branched or multicyclic). We give a new exact formula for the expected radius of gyration and contraction factor of GG in terms of the number of subdivisions of each edge of GG' and a new weighted Kirchhoff index for GG'. The formula explains and extends previous results for the contraction factor and Kirchhoff index of subdivided graphs.

Keywords

Cite

@article{arxiv.2503.01310,
  title  = {An exact formula for the contraction factor of a subdivided Gaussian topological polymer},
  author = {Jason Cantarella and Tetsuo Deguchi and Clayton Shonkwiler and Erica Uehara},
  journal= {arXiv preprint arXiv:2503.01310},
  year   = {2025}
}