Pelabelan Harmonis Ganjil pada Kelas Graf Baru Hasil Operasi Cartesian Product
DOI:
https://doi.org/10.15642/mantik.2017.3.2.87-95Keywords:
Cartesian product; Union graph; Odd harmonious graph; Snake-net graphAbstract
Graph class which has the characteristic of odd harmonious labeling is called as odd harmonious graph. Net graph is a graph which is gained by using operation Cartesian product of two line graphs. The construction of snake-net graph is inspired by the definition of snake graph replacing the round graph to net graph. In this paper, the study will show that snake-net graph fulfill the characteristic of odd harmonious graph in such a way snake-net graph is the odd harmonious graph. In the end of this paper, it is also shown that the union of snake-net graph is also called as the odd harmonious graph.
Downloads
Download data is not yet available.
References
[1] Abdel-Aal, M. E. New Families of Odd Harmonious Graphs. International Journal of Soft Computing, Mathematics and Control, 3(1), (2014) 1-13.
[2] Alyani, F., Firmansah, F., Giyarti, W., dan Sugeng, K. A. The Odd Harmonious Labeling of kCn-Snake Graphs for Spesific Values of n, that is, for n = 4 and n = 8. Proceeding IndoMS International Conference on Mathemathics and Its Applications, UGM dan IndoMS. (2013) 225-230. 6-7 November, Yogyakarta.
[3] Firmansah, F., dan Sugeng, K. A. Pelabelan Harmonis Ganjil pada Graf Kincir Angin Belanda dan Gabungan Graf Kincir Angin Belanda. Magistra, No 94 Th. XXVII, ISSN 0215-9511, (2015) 56-92.
[4] Firmansah, F. 2016. Pelabelan Harmonis Ganjil pada Gabungan Graf Ular dan Graf Ular Berlipat. Proceeding Konferensi Nasional Matematika dan Pembelajarannya (KNPMP 1) UMS. (2016) 809-818. 12 Maret, Surakarta.
[5] Firmansah, F. dan Syaifuddin, M. W. Pelabelan Harmonis Ganjil pada Graf Kincir Angin Double Quadrilateral. Proceeding Seminar Nasional Matematika dan Pendidikan Matematika, FKIP UNY, (2016) 53-58. 5 November, Yogyakarta.
[6] Firmansah, F. dan Yuwono, M. R. Odd Harmonius Labeling on Pleated of the Dutch Windmill Graphs. Cauchy – Jurnal Matematika Murni dan Aplikasi, 4(4). (2017) 161-166. p-ISSN: 2086-0382, e-ISSN: 2477-3344.
[7] Jeyanthi, P. dan Philo, S. Odd Harmonious Labeling of Some Cycle Related Graphs. Proyecciones Journal of Matematics, 35(1). (2016) 85-98.
[8] Jeyanthi, P., Philo, S. dan Sugeng, K.A. Odd Harmonious Labeling of Some New Families of Graphs. SUT Journal of Mathematics. 51(2). (2015) 53-65.
[9] Gallian, J. A. A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, 18. (2016) #DS6.
[10] Liang, Z., dan Bai, Z. On The Odd Harmonious Graphs with Applications, J. Appl. Math. Comput., 29, (2009) 105-116.
[11] Saputri, G. A., Sugeng, K. A., dan Froncek, D. The Odd Harmonious Labeling of Dumbbell and Generalized Prims Graphs, AKCE Int, J. Graphs Comb., 10(2), (2013) 221-228.
[12] Vaidya, S. K., dan Shah, N. H. Some New Odd Harmonious Graphs. International Journal of Mathematics and Soft Computing, 1(1), (2011) 9-16.
[2] Alyani, F., Firmansah, F., Giyarti, W., dan Sugeng, K. A. The Odd Harmonious Labeling of kCn-Snake Graphs for Spesific Values of n, that is, for n = 4 and n = 8. Proceeding IndoMS International Conference on Mathemathics and Its Applications, UGM dan IndoMS. (2013) 225-230. 6-7 November, Yogyakarta.
[3] Firmansah, F., dan Sugeng, K. A. Pelabelan Harmonis Ganjil pada Graf Kincir Angin Belanda dan Gabungan Graf Kincir Angin Belanda. Magistra, No 94 Th. XXVII, ISSN 0215-9511, (2015) 56-92.
[4] Firmansah, F. 2016. Pelabelan Harmonis Ganjil pada Gabungan Graf Ular dan Graf Ular Berlipat. Proceeding Konferensi Nasional Matematika dan Pembelajarannya (KNPMP 1) UMS. (2016) 809-818. 12 Maret, Surakarta.
[5] Firmansah, F. dan Syaifuddin, M. W. Pelabelan Harmonis Ganjil pada Graf Kincir Angin Double Quadrilateral. Proceeding Seminar Nasional Matematika dan Pendidikan Matematika, FKIP UNY, (2016) 53-58. 5 November, Yogyakarta.
[6] Firmansah, F. dan Yuwono, M. R. Odd Harmonius Labeling on Pleated of the Dutch Windmill Graphs. Cauchy – Jurnal Matematika Murni dan Aplikasi, 4(4). (2017) 161-166. p-ISSN: 2086-0382, e-ISSN: 2477-3344.
[7] Jeyanthi, P. dan Philo, S. Odd Harmonious Labeling of Some Cycle Related Graphs. Proyecciones Journal of Matematics, 35(1). (2016) 85-98.
[8] Jeyanthi, P., Philo, S. dan Sugeng, K.A. Odd Harmonious Labeling of Some New Families of Graphs. SUT Journal of Mathematics. 51(2). (2015) 53-65.
[9] Gallian, J. A. A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, 18. (2016) #DS6.
[10] Liang, Z., dan Bai, Z. On The Odd Harmonious Graphs with Applications, J. Appl. Math. Comput., 29, (2009) 105-116.
[11] Saputri, G. A., Sugeng, K. A., dan Froncek, D. The Odd Harmonious Labeling of Dumbbell and Generalized Prims Graphs, AKCE Int, J. Graphs Comb., 10(2), (2013) 221-228.
[12] Vaidya, S. K., dan Shah, N. H. Some New Odd Harmonious Graphs. International Journal of Mathematics and Soft Computing, 1(1), (2011) 9-16.
Downloads
Published
2017-10-28
How to Cite
Firmansah, F., & Yuwono, M. R. (2017). Pelabelan Harmonis Ganjil pada Kelas Graf Baru Hasil Operasi Cartesian Product. Jurnal Matematika MANTIK, 3(2), 87–95. https://doi.org/10.15642/mantik.2017.3.2.87-95
Issue
Section
Articles
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work
.png)
