Detecting the repetition of edge labelling from double mean labelling using path graphs

In this research article we examinedfew results on Double Mean Labelling on somewhere onthe path of the graphs. This content can be expanded to network graphs of higher dimensions, since each graph consists of a path. In previous theory we have proved the results under Double Mean Labelling on the path graph for all n. Here we compute the graph for the dimension of path graph with four vertices and split the vertex set into two subsets. Since we were approaching to find out the repetition of edge labelling, which can be removed from the collection of possibilities given from the theorem of Double Mean Labelling. After removing such possibilities using the concept of Detecting the edge labelling which tends to avoid the non-distinct edge labelling, where the concept is discussed with few theorems. This method gives us a minimization of repetition of edge labelling i.e., which reduces the duration of finding the non-distinct edge labelling. Also, we have introduced an algorithm to generate the label of a vertex from the vertex set.