New Results in Bi- Domination in Graphs

Abstract

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.

Keywords

• domination number
• bi-domination number
• minimum dominating set.