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

Abdul Gazir S, I Gede Adhitya Wisnu Wardhana, Ni Wayan Switrayni, Qurratul Aini


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

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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References


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