Possibilities of Edge Repetition using Double Mean Labeling

Abstract

In this research article we improvised for absolute detection of edge Labeling by finding out the ordered pairs for an edge label. There are some theorems proves the distinctiveness of the edge labels in previous articles. Suppose that, if all the adjacent nodes from the parent node receives equal value for the edges, such that, the parent node gets changes according to the adjacency of the parent node to achieve non-distinct edge values. Here, the label of the adjacent vertices is static and parent node splits into multifarious singleton vertex, which depends on the dimension n. Thus, the following theorem and proofs emerge from the idea of non-distinct edge labeling of the star graphs. Here we Constructed the Successor Vertex Graphs of Edge Recursion and the lemma is stated of how the vertex function looks for set of all ordered pairs of vertex label to achieve singleton edge labels using double mean labeling.