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The theory of domination and average total domination in graphs is a rich topic of investigation both from the point of view of theory and application. Computer science is branch in which use of the graph have become in dispensable, specifically, in problem, such as load balancing for massively parallel computer architectures. The main aim of this dissertation is to defined a new parameter namely average total domination number and is to studied for connected graphs and also we studied average total domination number for complete binary tree. Some bounds on average total domination number in terms of total domination number are also established.