DETOUR ENERGY OF COMPLEMENT OF SUBGROUP GRAPH OF DIHEDRAL GROUP

Authors

  • Abdussakir Abdussakir

DOI:

https://doi.org/10.30829/zero.v1i2.1460

Abstract

Study on the energy of a graph becomes a topic of great interest. One is the detour energy which is the sum of the absolute values of all eigenvalue of the detour matrix of a graph. Graphs obtained from a group also became a study that attracted the attention of many researchers. This article discusses the subgroup graph for several normal subgroups of dihedral groups. The discussion focused on the detour energy of complement of subgroup graph of dihedral group

References

Abdussakir, Akhadiyah, D. A., Layali, A., & Putra, A. T. (2017). Spektrum graf subgrup dan komplemen graf subgrup dari grup dihedral. Laporan Penelitian. Malang: Fakultas Sains dan Teknologi.

Abdussakir, Azizah, N. N., & Nofandika, F. F. (2009). Teori graf: Topik dasar untuk tugas akhir/skripsi. Malang: UIN Malang Press.

Anderson, D. F., Fasteen, J., & Lagrange, J. D. (2012). The subgroup graph of a group. Arab Journal of Mathematics, 1, 17-27.

Ayyaswamy, S. K., & Balachandran, S. (2010). On detour spectra of some graphs. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering, 4(7), 1038-1040.

Bhat, P. G., & D'Souza, S. (2015). Color Laplacian energy of a graph. Proceedings of the Jangjeon Mathematical Society, 18(3), 321-330.

Bhat, P. G., & D'Souza, S. (2017). Color signless Laplacian energy of graphs. AKCE International Journal of Graphs and Combinatorics, 14(2), 142-148.

Bondy, J. A., & Murty, U. S. R. (1976). Graph theory with applications. North-Holland. New York: Elsevier Science Publishing Co., Inc.

Bondy, J. A., & Murty, U. S. R. (2008). Graph theory. New York: Springer.

Chartrand, G., Lesniak, L., & Zhang, P. (2016). Graphs and Digraphs (6th ed.). Florida: CRC Press.

Das, K. C., Sorgun, S., & Xu, K. (2014). On Randic energy of graphs. MATCH Commun. Math. Comput. Chem, 72, 227-238.

Dummit, D. S., & Foote, R. M. (1991). Abstract Algebra. Englewood Cliffs, NJ: Prentice Hall.

Gilbert, W. J., & Nicholson, W. K. (2004). Modern algebra with applications. John Wiley & Sons, Inc. (2nd ed.). New Jersey: John Wiley & Sons, Inc.

Kakeri, F., & Erfanian, A. (2015). The complement of subgroup graph of a group. Journal of Prime Research in Mathematics, 11, 55-60.

Ramane, H. S., Revankar, D. S., Gutman, I., Rao, S. B., Acharya, B. D., & Walikar, H. B. (2008). Bounds for the distance energy of a graph. Kragujevac Journal of Mathematics, 31, 59-68.

Shabaf, S. R., & Fayazi, F. (2014). Laplacian Energy of a Fuzzy Graph. Iranian Journal of Mathematical Chemstry, 5(1), 1-10.

Xu, L., & Xu, X. (2016). On incidence energy of tree. Ars Combinatoria, 126, 93-107.

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Published

2023-07-25

Issue

Vol. 1 No. 2 (2017): July - December

Section

Articles

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