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

License

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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