The Spectrum Of Wheel Graph Using Eigenvalues Circulant Matrix

Hendra Cipta

doi:https://doi.org/10.14445/22315373/IJMTT-V66I6P520

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 6 | Year 2020 | Article Id. IJMTT-V66I6P520 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I6P520

The Spectrum Of Wheel Graph Using Eigenvalues Circulant Matrix

Hendra Cipta

Citation :

Hendra Cipta, "The Spectrum Of Wheel Graph Using Eigenvalues Circulant Matrix," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 6, pp. 198-204, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I6P520

Abstract

The purpose of this article is determining the spectrum of wheel graph. Some steps including drawing a wheel graph Wn, determining adjacency matrix of Wn and the eigenvalues of the circulant matrix of adjacency matrix are used. Furthermore, the spectrum of wheel graph is obtained based on the eigenvalues and its multiplicity. Spectrum of wheel graph Wn for W4,W6 and W8 are presented.

Keywords

wheel graph, spectrum graph, eigenvalues, circulant matrix.

References

[1] Chartnand, G and Lesniak, L, Graphs and Digraphs. Second Edition, California: A Division of Wadsworth Inc, 1996.
[2] Biggs, Norman, Algebraic Graph Theory Second Edition, Cambridge, 1993.
[3] Yin, Shuhua, Investigation On Spectrum Of The Adjacency Matrix And Laplacian Matrix Of Graph Gi. WSEAS Trans On System, 2008, pp. 362-372.
[4] Abdussakir, R.R. Elvierayani and M. Nafisah, On The Spectra Of Commuting And Non Commuting Graph On Dihedral Group, Cauchy-Jurnal Mat. Murni, 2017, pp. 176–182.
[5] Ayyaswamy, S.K.S, Balachandran, On Detour Spectra Of Some Graphs, Int J Math Compt Phys Electric Computing Eng, 2010, pp. 1038-1040.
[6] Rosen, Kenneth. H, Discrete Mathematics And Its Applications, Seventh Edition, New York: The McGraw-Hill Companies, Inc., 2012.
[7] Jain, S.K and Gunawardena, A.D, Linear Algebra An Interactive Approch, Unite States of America, 2004.
[8] Anton, Howard. and, Chris Rorres. Elementary Linear Algebra, Ninth Edition, John Wiley & Sons, Inc. All Rights Reserved, 2005.
[9] Wilson, Robin. J and Watkins, Graph And Introductory Approach. Singapore: Open University Course, 1990.
[10] Cvetkovic, Dragos, Applications Of Graph Spectra: An Introduction To The Literature. Mathematics Subject Classification, 2000.
[11] Cvetkovic, Dragos , Peter Rowlinson and Slobodan Simic, An Introduction To The Theory of Graph Spectra, New York : Cambridge, 2010.
[12] Gago, Silvia, Eigenvalue Distribution in Power Low Graphs. Aplimat Journal of Applied Mathmatics. 2008, pp. 29-35.
[13] Stevanovic, Dragan and Sanja Stevanovic, On Relation Between Spectra of Graphs And Their Digraph Decompositions. Publications De L’institut Mathématique, Nouvelle Série, Tome 85(99), 2009, pp. 47–54.
[14] Tee, Garry, Eigenvectors Of Block Circulant And Alternating Circulant Matrices. New Zealand Journal Of Mathematics. 2007, pp. 196-211.
[15] Wen, Fei, Qiongxiang Huang, Xueyi Huang and Fenjin Liu, The Spectral Characterization Of Wind-Wheel Graphs, Indian J. Pure Appl. Math., 2015, pp. 613-631.
[16] Zhang, Yuanping, Xiaogang Liu, Xuerong Yong, Which Wheel Graphs Are Determined By Their Laplacian Spectra?. Computers and Mathematics with Applications, 2009, pp. 1887-1890.