Wiener Number as an Immanant of the Laplacian of Molecular Graphs

In this work, we show that the Wiener number of an acyclic molecule may be expressed as a linear function of a hook immanant of the Laplacian matrix associated with the molecule. This relation leads to a new interpretation of the Wiener number as a weighted sum of matchings in the molecular graph of acyclic compounds. The connection between the Wiener number and immanants may pave the way for more use of algebraic tools in the study of the Wiener number.