M. N. Al-Harere ^{1, a)} and Athraa T. Breesam ^{2, b)}

¹ manal.n.alharere@uotechnology.edu.iq

² A.T.Breesam@gmail.com

^{a, b} Department of Applied Sciences,

University of Technology -Iraq

In this paper, some new results are introduced for the bi-domination in graphs. Some properties of bi-domination number and bounds according to maximum, minimum degrees, order, and size have been determined. The effects of removing a vertex and removing or adding an edge are discussed on the bi-domination number of a graph. This study is important to know affected graphs by the deletion or addition of components.