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You can say of a person that they are single/married/divorced/widowed, even that that person is a parent (father or mother). But is there a single word to refer to someone who is not a parent?
I can only think of some compounds such as childless or kidless, but I'm not sure if they convey the meaning proposed. I have read somewhere that there is an acronym but I don't know if it's widely used: DINK, but it refers to couples without kids (Double Income No Kids), not to a single person.