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.
Cantarella et al. (Tue,) studied this question.