Nilai Total Ketakteraturan Titik Dari m-Copy Graf Lingkaran
DOI:
https://doi.org/10.24014/jsms.v4i1.4518Abstract
Misalkan V=(G,E) adalah suatu graf dan adalah bilangan bulat positif. Pelabelan-k total pada graf dengan himpunan titik tak kosong V dan himpunan sisi E adalah pelabelan dari VUE ke {1,2,...,k}. Bobot suatu titik v adalah jumlah label titik v dan label semua sisi yang terkait dengan titik v. Suatu pelabelan-k total dikatakan tak teratur titik, jika bobot setiap titik berbeda. Nilai total ketakteraturan titik graf G (total vertex irregularity strength) adalah nilai k minimum atau label terbesar minimum yang digunakan untuk melabeli graf G dengan pelabelan total tak teratur titik. Hasil yang diperoleh dari penelitian ini adalah nilai total ketakteraturan titik dari graf m-copy graf Cn adalah pembulatan kebawah dari (nm+2)/3 dengan m bilangan bulat positif dan n kongruen dengan 2(mod3).References
Ahmad, A., Awan, K.M., Javaid, I., dan Slamin. “Total Vertex Irregularity Strength of Wheel Related Graphs”. Halaman 149. 2011.
Ahmad, A., Bača, M., dan Bashir, Y. “Total Vertex Irregularity Strength of Certain Classes of Unicyclic Graphs”. Halaman 2. 2014.
Amir, Z. “Matematika Diskrit”. Halaman 3-4,13, 28-32. Zanafa Publishing, Pekanbaru. 2010.
Ahmad, A., Bokhary, S.A.H., Hasni, R., dan Slamin. “Total Vertex Irregularity Strength of Ladder Related Graphs”. Halaman 2. 2014.
Bača, M., Jendrol J., Miller, M., dan Ryan, J. “On Irregular Total Labellings,” Discrete Math. Vol. 307, halaman 1378-1388. 2007.
Rajasingh, I., Rajan, B., dan Annamma,V. “On Total Vertex Irregularity Strength of Triangle Related Graphs”. Halaman 3. 2012.
Rajasingh, I., Rajan, B., dan Annamma,V. “On The Total Vertex Irregularity Strengths of Cycle Related Graphs and H Graphs”. Halaman 2. 2012.
Marzuki, C.C., Salman, A.N.M., dan Miller, M. “On The Total Irregularity Strength of Cycles and Paths”. Far East Journal of Mathematical Science. Vol. 82, halaman 11. 2013.
Marzuki, C.C., Fitria., Gianita, Nia., Fitri, Ramadana., dan Abdussakir “On The Total Irregularity Strength of of Cycle and of Path”. Far East Journal of Mathematical Science. Submitted.
Munir, R. “ Matematika Diskrit”. Edisi Tiga, halaman 353. Informatika Bandung, Bandung. 2007.
Nurdin, dkk. “On The Total Vertex Irregular Strength of a Disjoint Union of t Copies of a Path”. Halaman 2. 2009.
Nurdin, dkk. “On Total Vertex-Irregular Labellings of An Olive Tree and Their Copies”. Halaman 2. 2009.
Ramdani, R., Salman, A.N.M., dan Assiyatun, H. “On The Total Irregularity Strength of Regular Graphs,” Far East Journal of Mathematical Science. Vol. 47, Halaman 292-294. 2015.
Siang, J.J. “Matematika Diskrit dan Aplikasinya Pada Ilmu Komputer”. Edisi Empat, halaman 217. Andi, Yogyakarta. 2009.
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