Abstract: Problem Statement: A number of DNA computing models to solve mathematical graph problem such as the Hamiltonian Path Problem (HPP), Traveling Salesman Problem (TSP), and the Shortest Path Problem (SPP), have been proposed and demonstrated. Normally, the DNA sequences used for the computation should be critically designed in order to reduce error that could occur during a computation. Previously, we have proposed a DNA computing readout method tailored specifically to HPP in DNA computing using real-time Polymerase Chain Reaction (PCR). The DNA sequences were designed based on a procedure and DNASequenceGenerator was employed to generate the sequences required for the experiment. The drawback of the previous approach is that a pool of DNA sequences need to be generated by DNASequenceGenerator before the selection is done manually, based on several design constraints. Hence, an automatic and systematic approach is needed to generate the DNA sequences based on design constraints. Approach: In this study, a generate-and-test approach was proposed for the same problem subjected to several design constraints. The generateand-test algorithm consists of two main levels. The first level considered the basic constraints of DNA sequence design, which were melting temperature, GC-percentage, similarity, continuity, hairpin, and H-measure. This was followed by the second level that includes specific constraints formulated based