Affiliation:
1. SELÇUK ÜNİVERSİTESİ
2. ATATÜRK ÜNİVERSİTESİ
3. ERZURUM TEKNİK ÜNİVERSİTESİ
Abstract
The bitopologies have been associated with some knots in the literature with the help of a method called the knot digraph notation. The knot graphs and quasi pseudo metric spaces were used to obtain these bitopologies. With the help of quasi pseudo metrics, two topologies were obtained on a set. In this way, an association between some knots and bitopologies was established. The authors sought an answer to the question “Given the bitopologies associated with knots, can the knot itself be obtained ?” and they gave a method. This mentioned method consists of 6 steps.. In this work, it is shown in detail that according to the Alexander-Briggs notation, the reverse of the knot digraph notation is provided for the knots 3(1), 5(1), 5(2), 6(1), 6(2), 7(1), 7(2), 7(3), 8(1), 8(2), 8(3), 9(1), 9(2), 9(3), 10(1), 10(2), 10(3).
Reference7 articles.
1. Elmalı, C. S., Uğur, T. & Kunduracı, T. (2018). On New Knot Tables, The Third International Conference on Computational Mathematics and Engineering Sciences, Girne/Kıbrıs, https://doi.org/10.1051/itmconf/20182201019
2. Girija, B. & Pilakkat, R. (2013). Bitopological spaces associated with digraphs, South Asian Journal of Mathematics, Vol.3 (1), 56-65.
3. Kelley J.C. (1963). Bitopological Spaces, Proc. London Math., 13, 71-89.
4. Kunduracı, T. (2017) Düğüm Tabloları için Yeni Bir Metod: Düğüm Digraf Notasyonu, (Yüksek Lisans Tezi), Erzurum Teknik Üniversitesi, Matematik Anabilim Dalı, Erzurum.
Murasugi K. (1993), Knot Theory and Its Application, Boston: Birkhauser.
5. Uğur T., Elmalı C. S. & Yalaz F. (2018). The Reverse Operation Of Knot Digraph Notation, The Third International Conference on Computational Mathematics and Engineering Sciences, Girne/Kıbrıs, https://doi.org/10.1051/itmconf/20182201031.