# Hosoya Z Index and Correlation with Boiling Point

I have recently read about the Z topological index found by Hosoya. The papers/sources The Z index is the sum of the coefficients of the matching polynomials (no. of ways to choose an independent edge from the set of edges in the graph - if we let each carbon atom be a vertex and each bond between a pair of carbon atoms is an edge.). The paper states that in particular for alkanes or saturated hydrocarbons, there is a correlation found between the Z index (which measures the extent of branching - in what way??) and the boiling point (bp) of these alkanes.

I know that the bp of alkanes increases with its size (due to strong force of attractions). However, I am confused about how the Z index measures the extent of branching, and any underlying reasons that the Z index will correlate with the bp and other physiochemical properties.

For a given hydrocarbon C$_n$H$_{n+2}$ more branched hydrocarbons have lower boiling point. This is because they have less surface area to have Van der Waals interactions to entangle with each other (ropes have more chances to entangle with each other than balls). For example C(CH3)4 (n-pentane) is a gas, but all other pentanes are liquids.