The Intersection Graph of a Dihedral Group

Authors

  • Nurhabibah Nurhabibah Universitas Mataram
  • Abdul Gazir Syarifudin Universitas Mataram
  • I Gede Adhitya Wisnu Wardhana
  • Qurratul Aini Universitas Mataram

DOI:

https://doi.org/10.29303/emj.v4i2.119

Keywords:

The intersection graph, dihedral group, subgraph

Abstract

The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j  are said to be adjacent if and only if H_i \cap H_j \neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \gamma(\Gamma_{D_{2n}})=p. 

References

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Published

2021-12-30

How to Cite

Nurhabibah, N., Syarifudin, A. G., Wardhana, I. G. A. W., & Aini, Q. (2021). The Intersection Graph of a Dihedral Group. EIGEN MATHEMATICS JOURNAL, 4(2), 68–73. https://doi.org/10.29303/emj.v4i2.119

Issue

Vol. 4 No. 2 Desember 2021

Section

Articles

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All articles published in the Eigen Mathematics Journal will be available for free reading and downloading. The license applied to this journal is Creative Commons Attribution-Non-Commercial-Share Alike (CC BY-NC-SA).

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