Semnan UniversityInternational Journal of Nonlinear Analysis and Applications2008-682214520230501Some dominating results of the join and corona operations between discrete topological graphs235242679510.22075/ijnaa.2022.6795ENMays K.IdanDepartment of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, IraqMohammed A.AbdlhuseinDepartment of Mathematics, College of Education for Pure Sciences, University of Thi-Qar, Thi-Qar, IraqJournal Article20220105The dominating sets play an important role in applications of graph theory. In this field, some recent studies discussed the properties of the minimum dominating set ($\gamma $-set). The other type of study produces a topological space from the set of vertices or the set of edges of a graph. The previous paper introduces a new method to construct a graph $G_{\tau }$ from the topological space. In this paper, the dominating set and the domination number of $G_{\tau }$ are proved with their inverse. The domination number and inverse domination number of corona operation and join operation between two graphs are discussed.https://ijnaa.semnan.ac.ir/article_6795_6fab85f2d427ad9703f7dd710fd1e151.pdf