Present participle of divulge; the act of revealing or disclosing something secret.
From divulge + -ing (gerund/present participle suffix). The -ing suffix transforms any verb into its continuous form to show ongoing action.
Divulging is probably the most natural-sounding form of this word in modern English—'without divulging the secret' or 'she's divulging everything'—because the -ing form describes the action itself rather than putting it into a time frame.
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