RANK MINIMUM MATRIKS HERMITE YANG DIGAMBARKAN GRAF G

Penulis

  • Mohamad Syafii STKIP Kusumanegara Jakarta

DOI:

https://doi.org/10.24853/fbc.4.2.97-104

Kata Kunci:

Rank Minimum, Matriks Hermite, Graf, Matriks Adjacency.

Abstrak

Rank minimum dari matriks Hermite yang digambarkan oleh graf G didefinisikan dengan rank terkecil dari matriks Hermite suatu graf  G. Graf yang digunakan adalah graf komplit, graf lintasan, graf sikel, graf bipartisi komplit, dan graf star. Dalam menentukan rank minimum yang digambarkan graf tersebut dengan cara membuat matriks adjacency dari graf G tersebut, kemudian dikembangkan menjadi beberapa matriks Hermite, kemudian dicari rank dari beberapa matriks tersebut, sehingga diperoleh rank minimum. Dalam mencari rank matriks digunakan operasi baris elementer dan dibantu dengan program Matlab. Hasil penelitian ini diperoleh:

Referensi

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Chartrand, G. dan Ortrud, O. 1993. Applied and Algorithmic Graph Theory. Canada: McGraw-Hill Inc.

Chenette, Nathan L. dan Droms, S. V. 2007. “Minimum Rank of a Graph Over an Arbitrary Field”. Electronic Journal of Linear Algebra. Vol. 16, pp. 183-186.

Fallat, S. dan Hogben, L. 2007. “The Minimum Rank of Symmetric Matrices Described by a Graph: A Survey”. Linear Algebra and Its Applications. Vol. 462, pp. 558–582.

Leon, S. J. 2001. Aljabar Linear dan Aplikasinya. Jakarta: Erlangga.

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Wilson, R. J. dan Walkins, J. J.1990. Graphs an Intoductory Approach: A First Course in Discrete Mathematic. New York: John Wiley & Sons Inc.

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Diterbitkan

2018-12-31

Terbitan

Vol 4 No 2 (2018): FIBONACCI: Jurnal Pendidikan Matematika dan Matematika

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