Paired bondage in trees Original Research Article

Let image be a graph with image. A set image is a paired dominating set if image is dominating, and the induced subgraph image contains a perfect matching. The paired domination number of image, denoted by image, is the minimum cardinality of a paired dominating set of image. The paired bondage number, denoted by image, is the minimum cardinality among all sets of edges image such that image and image. We say that image is a image-strongly stable graph if, for all image, either image or image. We discuss the basic properties of paired bondage and give a constructive characterization of image-strongly stable trees.