Promulgate is a verb that means to declare something widely and officially. It can be one person spreading his or her belief of something or a government announcing a new policy.
It has two noun forms, promulgation and promulgator.
There are many differing ways to pronounce the vowel sounds in promulgate, and all are accepted as correct.
Propagate, besides being commonly misspelled with two o‘s, is a verb that means to create, usually when talking about vegetation, though sometimes it is used simply to mean that one thing causes another. It can also be a synonym of promulgate, to spread an idea or message.
It has two noun forms, propagation and propagator.
Bob and Roberta Smith is the cognomen of a British artist who specializes in humorously mocking art institutions and the conventional attitudes they tend to promulgate. [The New York Times]
The FBI, for example, targets the very Arab-American and Muslim-American communities it needs to work with if it hopes to find and neutralize home-grown violent extremists, including promulgating new rules on profiling that allow for the potential mapping of Arab- or Muslim-American communities. [Reuters]
The exclusivities of a patented drug allow for profits vastly greater than those likely with any supplement, and that monetary divide propagates a divide in related research evidence. [Huffington Post]
The wonders of twin-scaling – whereby bulbs are surgically-divided into a multitude of small slivers and grown on in relatively sterile conditions, allowing increased rates of propagation – has allowed the wide distribution of this exquisite plant, and it is now widely available at a respectable price. [The Guardian]