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