The spectrum on prism graph using circulant matrix

Authors

  • Triyani Triyani Universitas Jenderal Soedirman
  • Mashuri Mashuri Universitas Jenderal Soedirman
  • Bunga Tirai Anarkis Universitas Jenderal Soedirman
  • Slamet Riyadi Universitas Jenderal Soedirman

DOI:

https://doi.org/10.12928/bamme.v2i1.5129

Keywords:

Circulant matrix, Eigen value, Eigen vector, Regular graph, Spectral graph theory, Spectrum of a graph

Abstract

Spectral graph theory discusses about the algebraic properties of graphs based on the spectrum of a graph. This article investigated the spectrum of prism graph. The method used in this research is the circulant matrix. The results showed that prism graph P2,s is a regular graph of degree 3, for s odd and s ≥ 3, P2,s is a circulantt graph with regular spectrum.

References

Anton, H. (2005). Elementary Linear Algebra, 9th ed. Hoboken: John Wiley & Sons.

Baca, M., Bashir, F., & Semanicova, A. (2011). Face Antimagic Labelings of Antiprisms. Util Math 84, 209-224.

Biggs, N. (1993). Algebraic Graph Theory, Second edition. Boca Raton: Chapman & Hall/CRC.

Chartrand, G., & Lesniak, L. (1996). Graphs & Digraphs, Third Edition. Boca Raton: Chapman & Hall/CRC.

Cvetkovic, D., & Gutman, I. (2009). Applications of Graph Spectra. Belgrade and Kragujevac.

Gutman, I., Vidović, D., & Stevanović, D. P. (2002). Chemical applications of the Laplacian spectrum. VI On the largest Laplacian eigenvalue of alkanes. Journal of the Serbian Chemical Society, 67(6), 407-413.

Hasmawati. (2008). Spektrum Graph Lengkap dan Siklus. Jurnal Ilmiah Elektrikal Enjiniring UNHAS, 6(3).

Kolman, B. (2004). Elementary Linear Algebra 8th ed. New Jersey: Pearson Education.

Kristiana, R. W. (2010). Spektrum Graf Mobius Ladder. Thesis. Semarang: Universitas Negeri Semarang.

Maas, C. (1985). Computing and Interpreting the Adjacency Spectrum of Traffic Networks. Journal of Computational and Applied Mathematics, 459-466.

Prism graph P(2,s)

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Published

2022-05-18

Issue

Vol. 2 No. 1 (2022)

Section

Articles

License

Copyright (c) 2022 Triyani, Mashuri, Bunga Tirai Anarkis, Slamet Riyadi

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