Persamaan polinomial karakteristik matriks Adjacency, matriks Laplace, dan matriks Signless-Laplace graf multipartisi komplit K (α_1, α_2, α_3, ..., α_n)

Ikawati, Deasy Sandhya Elya (2013) Persamaan polinomial karakteristik matriks Adjacency, matriks Laplace, dan matriks Signless-Laplace graf multipartisi komplit K (α_1, α_2, α_3, ..., α_n). Undergraduate thesis, Universitas Islam Negeri Maulana Malik Ibrahim.

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Abstract

INDONESIA:

Pada saat mencari spectrum, nilai eigen sangat diperlukan. Oleh karena itu penulis meneliti tentang polinomial karakteristik, yang akan menghasilkan nilai eigen.

Untuk mencari polinomial karakteristik, penulis berangkat dari graf multipartisi komplit, yaitu graf yang terdiri dari banyak partisi dengan titik tiap partisi saling terhubung langsung, namun tidak menghubungkan titik pada satu partisi.

Setelah ditentukan graf, diperoleh matriks Adjacency, matriks Laplace L(G)=D(G)-A(G), dan matriks Signless-Laplace S(G)=D(G)+A(G).
Polinomial karakteristik adalah dengan adalah suatu matriks dan adalah matriks Identitas. Akar-akar dari polinomial tersebut adalah nilai eigen.
Berdasarkan pembahasan, diperoleh pola umum persamaan polinomial karakteristik :
1. Matriks Adjacency... yaitu...
2. Matriks Adjacency... yaitu:...
3. Matriks Laplace... yaitu:...
4. Matriks Laplace.... yaitu:...
5. Matriks Laplace... yaitu:....
6. Matriks Laplace....yaitu:...
7. Matriks Signless-Laplace... yaitu:...
8. Matriks Signless-Laplace... yaitu:...
9. Matriks Signless-Laplace... yaitu:...

ENGLISH:

At the time of seeking spectrum, eigenvalue indispensable. Therefore, the author examines the characteristic polynomial, which will produce an eigenvalue.

To find the characteristic polynomial, the authors depart from multipartisi complete graph, ie a graph that consists of multiple partitions with each partition dots are connected, but do not connect the dots on one part of the partition.

Once defined graphs, adjacency matrices obtained, Laplace matrix.... , and matrixSignless -Laplace.....
Characteristic polynomial is with A is a matrix and I is the identity matrix. The roots of the polynomial are the eigenvalues.
Based on the discussion, the general pattern obtained characteristic polynomial equation:
1. Adjacency Matrix is:....
2. Adjacency Matrix is:....
3. aplace Matrix is:....
4. Laplace Matrix is:....
5. Laplace Matrix is:....
6. Laplace Matrix is:....
7. Signless-Laplace Matrix is:.....
8. Signless-Laplace Matrix is: .....
9. Signless-Laplace Matrix is:....

Item Type: Thesis (Undergraduate)
Supervisor: Abdussakir, Abdussakir and Abidin, Munirul
Keywords: Graf Multipartisi Komplit; Matriks Adjacent; Matriks Laplace; Matriks Signless-Laplace; Polinomial Karakteristik;mComplete Multipartite Graf; Adjacent Matrix; Matrix Laplace-Laplace matrix Signless; Characteristic Polynomial
Subjects: 01 MATHEMATICAL SCIENCES > 0103 Numerical and Computational mathematics > 010301 Numerical Analysis
01 MATHEMATICAL SCIENCES > 0199 Other Mathematical Sciences > 019999 Mathematical Sciences not elsewhere classified
Departement: Fakultas Sains dan Teknologi > Jurusan Matematika
Depositing User: Ahmad Zaini
Date Deposited: 14 Jun 2017 04:31
Last Modified: 14 Jun 2017 04:31
URI: http://etheses.uin-malang.ac.id/id/eprint/7089

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