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.