On a group testing problem: Characterization of graphs with 2-complexity image and maximum number of edges Original Research Article

Consider the following generalization of the sequential group testing problem for 2 defective items, which is suggested by Aigner (1988) in : Suppose a graph image contains one defective edge image. Find the endpoints of image by testing whether a subset of vertices of cardinality at most 2 contains at least one of the endpoints of image or not. What is then the minimum number image of tests, which are needed in the worst case to identify image?