Novel results on partial hosoya polynomials: An application in chemistry

This article deal with an investigation of certain properties of partial Hosoya polynomial and then computing this new polynomial for some family of well-known graphs. Also, we verify some results concerning the zeros location of this polynomial in a ring shaped region. In this way, we include not only new results as special cases, but also improve the results due to Dehmer et al. [12] as a particular case. In continuing, the unique positive root of a new version of partial Hosoya polynomial has been evaluated. Finally, we explore some functional measures based on the complex zeros of partial Hosoya polynomials and then we compute the Pearson correlation between these measures and well-known topological indices. Our results show that these new measures have a linear correlation with the Wiener index.