In DNA sequencing, the fragment assembly gives the sense of putting all the fragments together to reconstruct a complete DNA sequence. The aim is to obtain the shortest or smallest DNA sequence that contains all the fragments as substrings. The motivation for the fragment assembly comes from next generation sequencing (NGS), which can’t directly sequence long contiguous stretches of DNA. Therefore, in this work, a novel approach is proposed for DNA sequencing in fragment assembly, drawing inspiration from the travelling salesman problem (TSP), trie data structure, and suffix trie. In this proposed approach, the first step is to identify overlaps between each pair of DNA fragments utilizing standard trie and suffix tries data structures. Subsequently, the shortest DNA sequence is determined by finding the Hamiltonian circuit with the maximum cost within a directed connected weighted graph, which is constructed by using a modified version of the TSP. Ultimately, an optimal assembled sequence is obtained as the final outcome of the proposed approach.