Determine whether each of the following graphs has a Hamiltonian circuit. If it does have an Hamiltonian circuit, find such a circuit. If it does not have an Hamiltonian circuit, explain why you can be 100% sure that it does not. 
Definitions:
Qualified Residence
A primary or secondary home that meets certain IRS criteria, allowing for potential mortgage interest deductions.
Deduction
An expense that can be subtracted from gross income to reduce the amount of income subject to income tax.
Taxpayer's Principal Residence
The primary dwelling a taxpayer lives in for a major portion of the year, which can qualify for certain tax benefits like the mortgage interest deduction.
Standard Business Mileage
The set rate per mile the IRS allows for deduction when an individual uses their personal vehicle for business purposes.
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