On the 3-restricted edge connectivity of permutation graphs Original Research Article

An edge cut image of a connected graph image is a image-restricted edge cut if image is disconnected, and every component of image has at least image vertices. The image-restricted edge connectivity is defined as the minimum cardinality over all image-restricted edge cuts. A permutation graph is obtained by taking two disjoint copies of a graph and adding a perfect matching between the two copies. The image-restricted edge connectivity of a permutation graph is upper bounded by the so-called minimum image-edge degree. In this paper some sufficient conditions guaranteeing optimal image-restricted edge connectivity and super image-restricted edge connectivity for permutation graphs are presented for image.