Relation between matrices and the suborbital graphs by the special number sequences

Authors

ÜMMÜGÜLSÜN AKBABA
ALİ HİKMET DEĞER

DOI

10.55730/1300-0098.3121

Abstract

under circuit and forest conditions. Special number sequences and special vertex values of minimal length paths in suborbital graphs have been associated in our previous studies. In these associations, matrix connections of the special continued fractions $\mathcal K (-1/-k)$, where $k\in \mathbb{Z}^{+}, \ k\geq 2$ with the values of the special number sequences are used and new identities are obtained. In this study, by producing new matrices, new identities related to Fibonacci, Lucas, Pell, and Pell-Lucas number sequences are found by using both recurrence relations and matrix connections of the continued fractions. In addition, the farthest vertex values of the minimal length path in the suborbital graph $\mathrm{\mathbf{F}}_{u,N}$ and these number sequences are associated.

Keywords

Pell numbers, Pell-Lucas numbers, Fibonacci numbers, Lucas numbers, continued fractions, suborbital graphs

First Page

753

Last Page

767

Recommended Citation

AKBABA, ÜMMÜGÜLSÜN and DEĞER, ALİ HİKMET (2022) "Relation between matrices and the suborbital graphs by the special number sequences," Turkish Journal of Mathematics: Vol. 46: No. 3, Article 6. https://doi.org/10.55730/1300-0098.3121
Available at: https://journals.tubitak.gov.tr/math/vol46/iss3/6