If the biological mother’s affidavit, required by section 43-104.09, identifies only one possible biological father of the child and states that there are no other possible biological fathers of the child, and if the named father executes a valid relinquishment and consent to adoption of the child in the form mandated by section 43-106 or executes a denial of paternity and waiver of rights in the form mandated by section 43-106, the court may enter a decree of adoption pursuant to section 43-109 without regard to sections 43-104.12 to 43-104.16. A named biological father’s relinquishment and consent or a named biological father’s waiver of rights is irrevocable upon signing and is not voidable for any period after signing. Such relinquishment and consent or such waiver of rights may only be challenged on the basis of fraud or duress for up to six months after signing.