image-Domination perfect trees Original Research Article

Let image and let image be a graph. According to Dunbar et al. [image-Domination, Discrete Math. 211 (2000) 11–26], a set image is an image-dominating set of G if image for all image. Similarly, we define a set image to be an image-independent set of G if image for all image. The image-domination number image of G is the minimum cardinality of an image-dominating set of G and the image-independent image-domination number image of G is the minimum cardinality of an image-dominating set of G that is also image-independent. A graph G is image-domination perfect if image for all induced subgraphs H of G. We characterize the image-domination perfect trees in terms of their minimally forbidden induced subtrees. For image there is exactly one such tree whereas for image there are infinitely many.