THE INTERSECTION GRAPH REPRESENTATION OF A DIHEDRAL GROUP WITH PRIME ORDER AND ITS NUMERICAL INVARIANTS

Abstract

One of the concepts in mathematics that developing rapidly today is Graph Theory. The development of Graph Theory has been combined with Group Theory, that is by representing a group in a graph. The intersection graph from group , noted by , is a graph whose vertices are all non-trivial subgroups of group  and two distinct vertices  are adjacent in  if and only if . In this research the intersection graph of a Dihedral  group, we looking for the shapes and numerical invariants. The results obtained are if  for , then  has a subgraphs  and  subgraphs , the girth of the graph  is 3, radius and diameter of the graph  in a row is 2 and 3, and the chromatic number of the graph  is