Hasil Kali Matriks (Mod 2) pada Graf Roda, Graf Pertemanan dan Graf Bunga

Fransiskus Fran, Novita Indah Saputri, Mariatul Kiftiah

Abstract


ABSTRAK

Pada artikel ini dibahas sifat-sifat hasil kali matriks (mod 2) terkait graf roda, graf pertemanan, dan graf bunga yang grafikal. Beberapa hasil yang diperoleh, A(Wn)A(Wn)(Mod 2) dan A(Wn)A(Sn)(Mod 2) grafikal apabila n=2k+1 dengan Sn merupakan graf bintang. Selanjutnya, diperoleh A(Wn)A(Go)(mod 2) dan A(Wn)A(G0)(mod 2) grafikal untuk semua n>=3 dengan G0 adalah subgraf dari Wn dengan degG0v0=0, degG0vl=degWnvl, untuk 1<= l <= n. Hasil kali matriks (mod 2) yang grafikal juga diperoleh untuk graf pertemanan dan graf bunga dengan komplemen dan subgrafnya masing- masing. Hasil lebih umum diperoleh untuk kondisi sehingga A(G)A(G)(mod 2) grafikal.

 

ABSTRACT

In this paper, we discussed the properties of the wheel, flower and friendship graphs for which the matrix product under modulo 2 was graphical. Let Sn be a star graph and G0 be a subgraph of Wn where degG0v0=0, degG0vl=degWnvl, for 1<= l <= n. We proved the matrix product A(Wn)A(Wo)(mod 2)  and A(Wn)A(Sn)(Mod 2) was graphical for n=2k+1 and the matrix product A(Wn)A(Go)(mod 2) and A(Wn)A(G0)(mod 2) was graphical for all n>=3. For the next, a graphical matrix product (mod 2) was also obtained for the friendship graph and the flower graph with its complement and subgraph, respectively. As more general results were obtained for conditions such that A(G)A(G)(mod 2) was graphical.


Keywords


Adjacency Matrix; Subgraph; Wheel Graph; Flower Graph; Friendship Graph; Matrix Product

Full Text:

PDF [INDONESIA]

References


H.S. Mehta and U.P. Acharya, “Adjacency Matrix of Product Graphs”, in International Conference on Research and Inventions in Science, Engineering & Technology. vol. 7, 2017, pp. 158-165.

K.M. Prasad, M. Sudhakara, H.S. Sujatha, and M. Vinay. "Matrix Product of Graphs", in Combinatorial Matrix Theory and Generalized Inverses of Matrices, R. B. Bapat, S. J. Kirkland, K. M. Prasad, and S. Puntanen, Eds. India: Springer India, 2013, pp. 41-56, 2013.

K.M. Prasad, M. Sudhakara, H.S. Sujatha, and K.V. Soumnya, “Matrix Product (Modulo 2) of Graphs”, Indian J. Pure Appl. Math., vol. 45, no. 6, pp. 851–860, Dec. 2014, doi: 10.1007/s13226-014-0093-4.

B. S. John and S. Jency, “Matrix Product (Modulo-2) Of Cycle Graphs”, International Journal of Mathematics and Statistics Invention, vol. 4, no. 7, pp. 8-13, sept. 2016.

B. S. John and S. Jency, “Matrix Product (Modulo-2) Of Petersen Graphs”, International Journal of Mathematics Archive, vol. 7, No. 8, pp. 139-143, 2016.

K. A. Bhat, K. M. Prasad, and G. Sudhakara, “Some Matrix Equestions of Graph”, Advances and Applications in Discrete Mathematics, vol. 17. No. 1, pp. 29-48, 2018.

K. A. Bhat and G. Sudhakara, “Commuting Graph and Their Generalized Complements”, Malaysian Journal of Mathematical Science, vol. 12, No.1, pp. 63-84, 2018.

K. A. Bhat and G. Sudhakara, “Commuting and Decomposition of K_(n_1,n_2,⋯,n_k ) through Realization of The Product A(G)A(G_k^p )”, Special Issue on Linear Algebra and Its Applications (ICLAA2017), Spec. Matrices; vol. 6, pp. 343-356, 2018.

N. I. Saputri, M. Kiftiah, and F. Fran, “Perkalian Matriks pada Graf Roda”, Buletin Ilmiah Mat.Stat dan Terapannya (Bimaster), vol. 9, No. 2, pp. 337-342, 2020.

R. Munir, Matematika Diskrit, Ed ke-3, Bandung: Informatika, 2010.

H. Y. Harsya, I. H. Agustin, and D. Dafik, “Pewarnaan Titik pada Operasi Graf Sikel dengan Graf Lintasan”, in Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, vol. 1, 2014, pp. 11-18.

N. Rahmawati and B. Rahajeng, “Dekomposisi Graf Sikel, Graf Roda, Graf Gir dan Graf Persahabatan”, MATHunesa, vol. 3, np. 3, pp. 64-71, 2014.

G. B. Mertzios and W. Unger, “The Friendship Problem on Graphs“, in 1st International Conference on Relations, Orders and Graphs : Interaction with Computer Science (ROGICS), 2008, pp. 152-158.

W. Abidin and Masni, “Pewarnaan Sisi pada Graf yang Berhubungan dengan Sikel”, Jurnal MSA, vol. 2 No. 1, pp. 69-75, 2014.




DOI: https://doi.org/10.34312/jjom.v3i2.10468



Copyright (c) 2021 Fransiskus Fran, Novita Indah Saputri, Mariatul Kiftiah

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.


Jambura Journal of Mathematics has been indexed by

>>>More Indexing<<<


Creative Commons License

Jambura Journal of Mathematics (p-ISSN: 2654-5616 | e-ISSN: 2656-1344) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Powered by Public Knowledge Project OJS. 


Editorial Office 

Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Gorontalo, Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango 96119, Gorontalo, Indonesia. Email: info.jjom@ung.ac.id.