Spectral Characteristics of The Antiadjacency Matrix of Kite Graph

Authors

  • Miming Fikria Camilla Department Mathematics, Universitas Indonesia, Indonesia
  • Melza Rensiana Department Mathematics, Universitas Indonesia, Indonesia
  • Denny Riama Silaban Department Mathematics, Universitas Indonesia, Indonesia

DOI:

https://doi.org/10.20956/j.v21i2.40490

Keywords:

Anti-adjacency matrix, spectrum, characteristic polynomial, complete graph, path

Abstract

Let G=(V,E)  be a connected graph, where V is the set of vertices and E is the set of edges of G. The kite graph, denoted by Kiten,m, is a graph obtained by appending a complete graph Kn to a pendant vertex of path Pm. This research investigates the spectrum of antiadjacency matrix of kite graph. The antiadjacency matrix of a graph G of order n is a square matrix with order n where the entries of the matrix represent the nonadjacency of the vertices.

 

References

[1] Aji, B.H., Sugeng, K. A., & Aminah, S., 2021. Characteristic polynomial and eigenvalues of antiadjacency matrix of directed unicyclic flower vase graph. Journal of Physics: Conference Series, 1722 (1). https://doi.org/10.1088/1742-6596/1722/1/012055

[2] Anzana, N., Aminah, S., & Silaban, D. R., 2020. Characteristic polynomial of anti-adjacency matrix of directed cyclic friendship graph. Journal of Physics: Conference Series, 1538 (1). https://doi.org/10.1088/1742-6596/1538/1/012007

[3] Bapat, R. B., 2010. Graphs and Matrices. New Delhi: Springer.

[4] Biggs, N., 1993. Algebraic Graph Theory 2nd ed. Cambridge: Cambridge University Press.

[5] Das, K. C., & Liu, M., 2016. Kite graphs determined by their spectra. Applied Mathematics and Computation. http://dx.doi.org/10.1016/j.amc.2016.10.032

[6] Hasyyati, N., Sugeng, K. A., & Aminah, S., 2021. Characteristic polynomial and eigenvalues of anti-adjacency matrix of directed unicyclic corona graph. Journal of Physics: Conference Series, 1836 (1). https://doi.org/10.1088/1742-6596/1836/1/012001.

[7] Irawan, W., & Sugeng, K. A, 2022. Characteristic Antiadjacency Matrix of Graph Join. BAREKENG: Jurnal Ilmu Matematika dan Terapan, Vol. 16, No.1, pp. 41-46.

[8] Meljbro, L., 2011. Methods for Finding (Real or Complex) Zeros in Polynomials.

[9] Meyer, C. D., 2000. Matrix Analysis and Applied Linear Algebra. SIAM.

[10] Petersen, K. B., & Pedersen, M. S., 2012. The Matrix Cookbook.

[11] Prayitno, M. I. A., Utama, S., & Aminah, S., 2019. Properties of anti-adjacency matrix of directed cyclic sun graph. IOP Conference Series : Materials Science and Engineering, 567 (1). https://doi.org/10.1088/1757-899X/567/1/012020

[12] Putra, G. L., 2024. Characteristic Polynomial and Spectrum of Antiadjacency Matrix for Graph K_m∘K_1 and H_m∘K_1. SITEKIN: Jurnal Sains, Teknologi dan Industri, Vol. 21, No. 2, pp. 357-361.

[13] Sorgun, S., & Topcu, H., 2016. On the Spectral Characterization of Kite Graphs. Journal of Algebra Combinatorics Discrete Structures and Applications.

[14] Yin, J., Zhao, H., Ma, X., Liang, J., 2022. On Spectral Characterization of Two Classes of Unicycle Graphs. Symmetry, 14(6), 1213. https://doi.org/10.3390/sym14061213

Downloads

Published

2025-01-12

How to Cite

Camilla, M. F., Rensiana, M., & Silaban, D. R. (2025). Spectral Characteristics of The Antiadjacency Matrix of Kite Graph. Jurnal Matematika, Statistika Dan Komputasi, 21(2), 345–353. https://doi.org/10.20956/j.v21i2.40490

Issue

Section

Research Articles