Properti Eigen Untuk Graf k-Regular Tak Terhubung

R. Respitawulan

Abstract


Abstract. (eigen properties of non-connected k-regular graph) One of the important properties of an adjacency matrix as a representation of a graph is its eigen property. According to Biggs, a k-regular connected graph will have k as one of its Eigen value and the multiplicity is 1. Here, we investigate the Eigen value and its multiplicity of a non-connected
k-regular graph. The result shows if a non-connected k-regular graph has c components, then will be one of its eigen value with the geometric multiplicity of c.

Keywords: adjacency matrix, eigen values, geometric multiplicity

Abstrak. Salah satu sifat penting dari matriks adjasen sebagai representasi dari graf adalah sifat eigennya. Biggs menyatakan bahwa graf regular terhubung dengan derajat k akan memiliki nilai eigen k yang multiplisitasnya satu. Di sini diselidiki nilai eigen untuk graf k-regular yang tak terhubung. Jika graf k-regular tak terhubung memiliki c buah komponen, maka k akan menjadi salah satu nilai eigen graf tersebut dengan multiplisitas geometri c.

Kata kunci: matriks adjasen, nilai eigen, multiplisitas geometri


References


Biggs, N. (1974). Algebraic Graph Theory. London: Cambridge Univ. Press

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Cvetkovic, D. M., Doob, M., and Sachs, H. (1995). Spectra of Graphs, Third Edition. Johann Ambrosius Barth Verlag.

Roberts, F. (1987). Graph Theory and Its Applications to Problems of Society, SIAM.

Tinkler, K. (1972). The physical interpretation of eigenvalues of dichotomous matrix. Inst. Brit. Geogr. Puli., Vol. 55, pp. 17-46.

Wilf, H. S. (1967). The Eigenvalues of A Graph and Its Chromatic Number, J. London Math. Soc. Vol. 42, pp. 330-332.




DOI: https://doi.org/10.29313/jmtm.v16i2.2691

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