DOI: https://doi.org/10.14710/jfma.v3i1.7413

SOME PROPERTIES OF COPRIME GRAPH OF DIHEDRAL GROUP D_2n WHEN n IS A PRIME POWER

Abdul Gazir S  -  Departement of Mathematics, Universitas Mataram, Indonesia
*I Gede Adhitya Wisnu Wardhana  -  Departement of Mathematics, Universitas Mataram, Indonesia
Ni Wayan Switrayni  -  Departement of Mathematics, Universitas Mataram, Indonesia
Qurratul Aini  -  Departement of Mathematics, Universitas Mataram, Indonesia

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Abstract

The Study of algebraic structures, especially on graphs theory, leads to a
new 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.

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Section: FUNDAMENTAL MATHEMATICS AND APPLICATIONS
Language : EN
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