On the Structural Non-identifiability of Flexible Branched Polymers

Abstract

The dynamics and statics of flexible polymer chains are based on their conformational entropy, resulting in the properties of isolated polymer chains with any branching potentially being characterized by Gaussian chain models. According to the graph-theoretical approach, the dynamics and statics of Gaussian chains can be expressed as a set of eigenvalues of their Laplacian matrix. As such, the existence of Laplacian cospectral trees allows the structural nonidentifiability of any branched flexible polymer.

Keywords

• Gaussian chain
• branched polymer
• graph theory
• tree
• cospectral graph
• Laplacian matrix
• Rouse matrix
• Zimm matrix