The Intersection Graph of a Dihedral Group

Nurhabibah Nurhabibah, Abdul Gazir Syarifudin, I Gede Adhitya Wisnu Wardhana, Qurratul Aini

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.

 


Keywords


The intersection graph, dihedral group, subgraph

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References


David, S Dummit, and Foote, Richard M. 2004. Abstract Algebra. New Jersey: Division of Simon & Schauster, Inc.

Fraleigh, J. B. 2014. A First Course in Abstract Algebra, Seventh Edition. United States of America : Pearson Education Limited.

Gazir, A. S., Wardhana, I G. A. W. 2019. Subgrup Nontrivial dari Grup Dihedral. Eigen Mathematic Journal, Vol.2 No.2.

Juliana, R., Masriani, Wardhana, I.G.A.W., Switrayni, N.W., and Irwansyah, 2020, Coprime graph of integers modulo n group and its subgroups, Journal of Fundamental Mathematics and Applications (JFMA) 3 (1), 15-18.

Masriani, Juliana, R., Syarifudin, A.G., Wardhana, I.G.A.W., Irwansyah, and Switrayni, N.W., 2020, Some Result of Non-Coprime Graph of Integers Modulo n Group for n a Prime Power, Journal of Fundamental Mathematics and Applications (JFMA) 3 (2), 107-111.

Misuki, W.U., Wardhana, I.G.A.W., Switrayni, N.W., and Irwansyah, 2021, Some Results of Non-Coprime Graph of The Dihedral Group D_2n for n a Prime Power, AIP Conference Proceedings 2329, 020005 (2021).

Murugesan, N., D.S. Nair. 2011. The Domination and Independence of Some Cubic Bipartite Graphs. International Journal Contemporer Math Sciences, Vol.6. No. 13.

Nurhabibah, Syarifudin, A.G., and Wardhana, I.G.A.W., 2021, Some Results of The Coprime Graph of a Generalized Quaternion Group Q_4n, Indonesian Journal of Pure and Applied Mathematics 3 (1), pp. 29-33

Shahsavari, H., B. Khosravi. 2017. On The Intersection Graph of a Finite Group. Czechoslovak Mathematical Journal, Vol. 67 No. 4.

Syarifudin, A.G., Nurhabibah, Malik, D.P. and, Wardhana, I.G.A.W., Some characterizatsion of coprime graph of dihedral group D_2n, J. Phys.: Conf. Ser. 1722, 012051.

Syarifudin A.G., and Wardhana, I.G.A.W., 2021, Beberapa Graf Khusus Dari Grup Quaternion, Eigen Mathematics Journal 4 (1), pp. 1-7.




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

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