In real life, it is always an urge to reach our goal in minimum effort i.e., it should have a minimum constrained path. The path may be shortest route in practical life, either physical or electronic medium. The scenario is to represents the ambiance as a graph and to find a spanning tree with custom design criteria. Here, we have chosen a minimum degree spanning tree, which can be generated in real time with minimum turnaround time. The problem is NP-complete in nature [1, 2]. The solution approach, in general, is approximate. We have used a heuristic approach, namely hybrid genetic algorithm (GA), with motivated criteria of encoded data structures of graph. We compare the experimental result with the existing approximate algorithm and the result is so encouraging that we are interested to use it in our future applications.