Improving bounds on link failure tolerance of the star graph

Determination of the minimum number of faulty links, image, that make every image-dimensional sub-star graph image faulty in an n-dimensional star network image, has been the subject of several studies. Bounds on image have already been derived, and it is known that image. Here, we improve the bounds on image. Specifically, it is shown that image, where image is the minimum number of faulty nodes that make every image faulty in image. The complexity of image is shown to be image which is an improvement over the previously known upper bound of image; this result in a special case leads to image, settling a conjecture introduced in an earlier paper. A systematic method to derive the labels of the faulty links in case of image is also introduced.