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Graph theory is branch of science, which has a wide application in fields of Engineering,Science and management. Graph theory enables us to represent any data in the form of nodes and the relations between them. Now a days as data is increasing exponentially it is very difficult to manage and analyze them, where one has to find all the possibilities and combinations like in the field of Networking, Bio-Technology, Database Management etc. Data may change their behavior very frequently, and it is time consuming to start all the calculation from the starting in this Dynamic Graph. Here we have proposed one approach to minimize time complexity for this type of graph, just by focusing on the affected part of the Graph.