On topological spaces generated by graphs and vice versa

Abstract

The relationship between Graph Theory and Topological Space has recently developed greatly , as researchers have been able to find
 solutions to some problems in daily life by transforming the problem
 into a graph and then generating a topological space and thus facilita-
 ting reading the problem and solving it. The researchers also studied
 the generation of graph from topological spaces.In this article we will present two types of relations on the edges set that generate topolog-
 ical spaces, and we will discuss some properties of this topology, and
 we will study discuss the method of returning from the topological
 space to the graphs through using previous relationships.

r-Domination Number for Some Special Graphs

“…The open neighborhood of a vertex 𝑤 is the set 𝑁(𝑤) = {𝑢 ∈ 𝑉, 𝑢𝑤 ∈ 𝐸(𝐺) } and closed neighborhood is the set 𝑁[𝑢] = 𝑁(𝑢) ∪ {𝑢}. Graph theory has several topics for more information about it see [1][2][3]. The study of domination problem is grown fast in graph theory.…”