Journal of Prime Research in Mathematics

# DG-domination topology in Digraph

Khalid Sh. Al’Dzhabri$$^{a,*}$$, Ahmed A. Omranr$$^{b}$$, Manal N. Al-Harere$$^c$$
$$^a$$Department of Mathematics, College of Education, University of AL Qadisiyha, Iraq.
$$^b$$Department of Mathematics, College of Education for Pure Science, University of Babylon, Iraq.
$$^c$$Department of Applied Sciences, University of Technology, Baghdad, Iraq.
Correspondence should be addressed to: Khalid Sh. Al’Dzhabri at khalid.aljabrimath@qu.edu.iq

### Abstract

Throughout this paper, a new entry from domination approaches is introduced which is called a $$DG-$$ dominating set and which builds its dominance by the topology that relates to digraphs called $$\tau _{DG}-$$ Topological space. Also, a modern definition of domination number called $$DG-$$domination number is created. Moreover, some properties of $$DG-$$ dominating set are presented. Finally, the $$DG-$$domination number for certain graphs are determined.

#### Keywords:

Topology, digraphs, $$DG-$$dominating set, $$DG-$$domination number.