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Your parents will not qualify you as HOH. You must have a dependent child in order to claim HOH.
In order to claim ANYONE, they have to have a social security number, their income must be less than $3100 and you had to provide more than 50% of their support during the year.
Since your parents only visited you for a short time, it does not sound like they qualify for dependent status.
Let me know if you do not understand or if you still have questions.
In order for you to claim them, they would have to have an ITIN# XXXXX a SSN.
Your status does not determine whether or not you can claim dependents. A single person can claim dependents if the dependent meets the criteria.