Radius, Diameter, Multiplisitas Sikel, dan Dimensi Metrik Graf Komuting dari Grup Dihedral
DOI:
https://doi.org/10.15642/mantik.2017.3.1.1-4Keywords:
Diameter; Cylce multiplicity; Metric dimension; Commuting graph; Dihedral groupAbstract
Commuting graph C(G) of a non-Abelian group G is a graph that contains all elements of G as its vertex set and two distinct vertices in C(G) will be adjacent if they are commute in G. In this paper we discuss commuting graph of dihedral group D2n. We show radius, diameter, cycle multiplicity, and metric dimension of this commuting graph in several theorems with their proof.
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References
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[2] Abdussakir, N. N. Azizah, and F. F. Novandika, Teori graf. Malang: UIN Malang Press, 2009.
[3] J. Vahidi and A. A. Talebi, “The commuting graphs on groups D2n and Qn,” J. Math. Comput. Sci., vol. 1, no. 2, pp. 123–127, 2010.
[4] T. T. Chelvam, K. Selvakumar, and S. Raja, “Commuting graphs on dihedral group main results,” J. Math. Comput. Sci., vol. 2, no. 2, pp. 402–406, 2011.
[5] H. Rahayuningtyas, A. Abdussakir, and A. Nashichuddin, “Bilangan kromatik graf commuting dan non commuting grup dihedral,” CAUCHY, vol. 4, no. 1, pp. 16–21, 2015.
[6] J. A. Bondy and U. S. R. Murty, Graph theory with applications. New York: Elsevier Science Publishing Co., Inc, 1976.
[7] M. M. A. Ali and S. Panayappan, “Cycle multiplicity of total graph of Cn, Pn, and K1,n,” Int. J. Eng. Sci. technology, vol. 2, no. 2, pp. 54–58, 2010.
[8] C. Hernando, M. Mora, I. M. Pelayo, C. Seara, and D. R. Wood, “Extremal graph theory for metric dimension and diameter,” Electron. J. Comb., vol. 17, no. 1, pp. 1–28, 2010.
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Published
2017-10-26
How to Cite
Abdussakir, A. (2017). Radius, Diameter, Multiplisitas Sikel, dan Dimensi Metrik Graf Komuting dari Grup Dihedral. Jurnal Matematika MANTIK, 3(1), 1–4. https://doi.org/10.15642/mantik.2017.3.1.1-4
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