On Some Connections Between Suborbital Graphs and Special Sequences

Year 2018, Volume: 10, 134 - 143, 29.12.2018

Ümmügülsün Akbaba Ali Hikmet Değer Tuğba Tuylu

Abstract

In this work, we used the terms of identity alternate sequence and also the even terms of alternate

sequences of Fibonacci and Lucas, the famous number sequences, to establish connections with the special vertex

values of the paths of minimal length in the suborbital graphs. These types of vertices also give rise to special

continued fractions, hence from recurrence relations for continued fractions, values of these vertices and values of

these special sequences were associated.

Keywords

Suborbital Graphs, Fibonacci Sequences, Lucas Sequences, Continued Fractions

References

• Akbas, M., On suborbital graphs for the modular group, Bull. London Math. Soc., 33, (2001), 647-652
• Cuyt, A., Petersen, V.B., Verdonk,B., Waadeland, H., W.B., Jones, Handbook of Continued Fractions for Special Functions, Springer, NewYork, 2008.
• Deger, A.H., Besenk, M., Guler, B.O., On suborbital graphsand related continued fractions, Applied Mathematics and Computation, 218(2011), 746-750.
• Deger, A.H., Vertices of paths of minimal lengths on suborbital graphs, Filomat, 31 (2017), 913-923.
• Deger, A.H., Relationships with the Fibonacci numbers and the special vertices of the suborbital graphs, Gümüşhane Üniversitesi Fen BilimleriEnstitüsü Dergisi, 7(2017),168-180.
• Drmota, M., Fibonacci numbers and continued fraction expansions, in Applications on Fibonacci Numbers, Springer, Scotland, 4 (1993),185-197.
• Jones, G.A., Singerman D., Wicks K., The modular group and generalized Farey graphs, London Math. Soc. Lecture Note Ser., 160, (1991),316-338.
• Koshy, T., Fibonacci and Lucas numbers with applications, A Wiley- Interscience Publication, Canada, 2001.
• Kushwaha, S., Sarma, R., Continued fractions arising from F1;2, The Ramanujan Journal, 46 (2018), 605-631.
• Sims, C.C., Graphs and finite permutation groups, Math. Zeitschr., 95, (1967), 76-86.