Domination in partitioned graphs with minimum degree two Original Research Article

Let image be a partition of the vertex set in a graph image. For image, let image denote the least number of vertices needed in image to dominate image. It is known that if image has order image and minimum degree two, then image. In this paper, we characterize those graphs of order image which are edge-minimal with respect to satisfying the conditions of connected, minimum degree at least two, and image.