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 D, noted by [Formula Presented], is a graph whose vertices are all non-trivial subgroups of group D, and two distinct vertices[Formula Presented] are adjacent in [Formula Presented] if and only if [Formula Presented]. In this research the intersection graph of a Dihedral [Formula Presented] group, we looking for the shapes and numerical invariants. The results obtained are if [Formula Presented] for k ≥2, then [Formula Presented] has a subgraphs [Formula Presented] and n subgraphs [Formula Presented], the girth of the graph [Formula Presented] is 3, radius and diameter of the graph [Formula Presented] in a row is 2 and 3, and the chromatic number of the graph [Formula Presented] is [Formula Presented].