Total restrained domination numbers of trees Original Research Article

For a given connected graph image, a set image is a total restrained dominating set if it is dominating and both image and image do not contain isolate vertices. The cardinality of the minimum total restrained dominating set in image is the total restrained domination number and is denoted by image. In this paper we characterize the trees with equal total and total restrained dominating numbers and give a lower bound on the total restrained dominating number of a tree image in terms of its order and the number of leaves of image.