The Study of algebraic structures, especially on graphs theory, leads to anew topics of research in recent years. In this paper, the algebraic structures that will be represented by a coprime graph are the dihedral group and its subgroups. The coprime graph of a group G, denoted by \Gamma_D_2n is a graph whose vertices are elements of G and two distinct vertices a and b are adjacent if only if (|a,|b|)=1. Some properties of the coprime graph of a dihedral group D_2n are obtained. One of the results is if n is prime then \Gamma_D_2n is a complete bipartite graph. Moreover, if n is the power of prime then \Gamma_D_2n is a multipartite graph.
Research on an algebraic structure represented in graph theory opens the way for new research in recent years. Several types of new graphs continue to be developed, such as coprime and non-coprime graphs. This article will represent the quaternion group in several graphs, such as coprime graphs, non-coprime graphs, commuting graphs, non-commuting graphs, and identity graphs. We obtained several theorems about unique graphs. One of the results is that non-coprime graphs from the quaternion group are complete and regular graphs.
Research on an algebraic structure represented in graph theory opens the way for new research in recent years. Several types of new graphs continue to be developed, such as coprime and non-coprime graphs. This article will represent the quaternion group in several graphs, such as coprime graphs, non-coprime graphs, commuting graphs, non-commuting graphs, and identity graphs. We obtained several theorems about unique graphs. One of the results is that non-coprime graphs from the quaternion group are complete and regular graphs.
Grup adalah sebuah pasangan terurut pada sebuah himpunan tak kosong yang memenuhi sifat asosiatif, memiliki invers dan identitas. Grup torsi adalah suatu grup yang setiap elemennya berorde hingga. Grup torsi erat kaitanya dengan grup siklik, bagaimana hubungan keduanya, apakah unsur grup torsi pada C* dan apa pembangun dari C* akan dibahas dalam makalah ini..
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