In discrete mathematics, topological sorting is very important, especially when working with directed acyclic graphs (DAGs). Optimizing topological sorting methods is important for making computers work faster in many situations, such as when planning tasks, figuring out dependencies, and designing circuits. This paper looks at how permutations can be used to make topological sorting better by using their structure features to make computations simpler. We proposed a new technique that improves contemporary topological sorting algorithms via the use of permutation-based totally upgrades. The advised way seems for traits in the structure of the layout and uses permutation groups to arrange the nodes, slicing down on processing steps that aren’t wished.  The suggested method is an awful lot quicker than well-known algorithms, especially while running with huge graphs, as shown via both theoretical evaluation and testing consequences. This study gives us a fresh look at topological sorting and helps us figure out how to make algorithms work better in real-life situations where time and computer power are limited.