Some characterizatsion of coprime graph of dihedral group D <sub>2n </sub>
Abdul Gazir Syarifudin, Nurhabibah, Deny Putra Malik, I Gede Adhitya Wisnu Wardhana
Abstract
Abstract The Coprime graph of group G denoted Γ G is a graph with vertices is an element of G, and two distinct vertices are adjacent when its order relative prime. In 2020, Gazir et al. give some characterizations of Γ D 2 n for n a prime power. The method that uses in this paper is deductive proof by taking some example of a coprime graph of D 2 n , then generalized the characterization of example. This paper gives some characteristics of the coprime graph of a dihedral group for more general cases. One of the result, Γ D 2 n is a multipartite graph with girth 3, radius 1, and diameter 2.
Topics & Concepts
Coprime integersCombinatoricsMathematicsDihedral groupGraphDihedral angleDiscrete mathematicsEdge-transitive graphPrime powerGraph powerPrime (order theory)Group (periodic table)Line graphPhysicsHydrogen bondQuantum mechanicsMoleculeFinite Group Theory ResearchGraph Labeling and Dimension ProblemsRings, Modules, and Algebras