Which item is installed on propane cylinders to allow excess pressure to escape?

The correct choice is the relief valve because it is specifically designed to prevent excessive pressure build-up within propane cylinders by allowing excess pressure to escape safely. When the internal pressure exceeds a certain pre-determined level, the relief valve opens and discharges gas, thus preventing potential cylinder rupture or explosion. This safety mechanism is critical in maintaining the integrity of the cylinder under varying temperature and pressure conditions.

Other options, while they might be related to pressure management or safety features in different contexts, do not serve the same primary function as a relief valve in propane cylinders. A purge valve, for instance, is typically used to allow the intentional release of gas for system maintenance or to clear fuel lines rather than to manage excess pressure. A blowout disk is designed to rupture under specific pressure thresholds but is not adjustable, and a frangible plug similarly serves a pressure-release function but is typically nondiscriminating in pressure thresholds. Thus, the relief valve is the appropriate component for safely managing excess pressure in propane cylinders.