Let  be a graph of order p and size q. For each edge  an edge weight  The edge degree weight sum of G (edge weight of G) is defined [9] by    In this paper, we introduce generalization ofedgedegreeweight sum by taking

  and 

The paper is a compilation of evaluation of the weights (for n = 1) of collection of different graphs. This labeling possesses values of  for line graph, total graph, middle graph, vertex identification graph, quasi-vertex total graph, subdivision graph, rooted graph, bistar  graph, banana tree, lotus graph, neighborhood graph, quadric graph, generalized Peterson graph and corona of two graphs.

edge weight, edge degree weight sum, vertex labeling.