The independence number of a graph which is just the cardinality of a largest independent vertex set, ie, the size of a maximum independent vertex set, is one of the many numbers associated with graphs and it has many applications in many problems including massive data sets, coding theory and wireless networks. Edge and vertex numbers are two of the most important graph parameters and most of the calculations related to graphs are done by means of them. Deleting vertices and edges naturally effects the calculations. In this work, it has been shown that the effect of these deletions also effect the independence number of graphs and these changes are calculated.