The Constructions of the Square Complex of a Diagram Group from a Graphical Presentation

In this paper, we may obtain diagram groups for any given graphical presentation. These groups can be viewed as the fundamental group of squire complexes. Let 4  be a semigroup presentation. The problems are divided into several cases according to the length of words, with all vertices in 4  being words of the length . The main aim of this article is to construct the connected square complex graph 4  of a diagram group from semigroup presentation 4 . Then we will prove 4  is the covering squire complexes for 4  for all . Then the covering space is identified for all connected square complex graphs by picking normal subgroups from the diagram group that was previously obtained from the semigroup presentation. This research introduces how to associate  with the covering space 4 , how to determine the generators for covering space 4 , and what 4  looks like