This paper presents a Discrete Particle Swarm Optimization (DPSO) technique to solve Graph based Travelling Salesman Problem (TSP). TSP can be represented as a graph where nodes represent cities and edges represent paths between them. A partially connected graph addresses a more realistic problem than a completely connected graph since in real life paths may not exist between certain cities. A novel approach to DPSO is used to obtain results in this situation. Convergence of DPSO to the optimal solution for such a Graph based TSP is tasted.