If the vertical fin of a single engine propeller-driven airplane is rigged properly, it will generally be parallel to:

When the vertical fin of a single-engine propeller-driven airplane is rigged properly, it being parallel to the vertical axis is crucial for the airplane's stability and control. The vertical fin, or vertical stabilizer, is designed to provide directional stability and control by opposing side forces, such as those encountered during yawing motions.

Aligning the fin with the vertical axis ensures that the aircraft maintains balanced flight without unwanted yawing tendencies. Any misalignment could lead to adverse handling characteristics, making it difficult for pilots to maintain control, especially in turbulent conditions or while executing maneuvers.

In contrast, while the longitudinal axis, horizontal axis, and center of gravity are all important concepts in aircraft design and performance, they don't specifically pertain to the proper rigging of the vertical fin. The longitudinal axis runs from the nose to the tail of the aircraft, the horizontal axis relates to pitch stability, and the center of gravity is about balancing the aircraft in terms of weight distribution. However, none of these alignments affect the functionality of the vertical fin as directly as its alignment with the vertical axis does in preserving directional stability.