It is always an urge to reach the 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 can be represented as a graph. Here, we have chosen a degree constrained spanning tree, which can be generated in real time in minimum turn-around time. The problem is obviously NP-complete in nature. 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 and also directed mutation is incorporated with it and the result is so encouraging, that we are interested to use it in our future applications. © Springer International Publishing Switzerland 2014.