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

Değer A. H., Akbaba Ü.

TURKISH JOURNAL OF MATHEMATICS, vol.46, pp.753-767, 2022 (SCI-Expanded)

  • Publication Type: Article / Article
  • Volume: 46
  • Publication Date: 2022
  • Doi Number: 10.55730/1300-0098.3121
  • Journal Name: TURKISH JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.753-767
  • Karadeniz Technical University Affiliated: Yes

Abstract

Continued fractions and their matrix connections have been used in many studies to generate new identities.
On the other hand, many examinations have been made in the suborbital graphs 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 K(−1/ − k) , where
k ∈ Z+, k ≥ 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 Fu,N and these number sequences are associated.
Key words: Pell numbers, Pell-Lucas numbers, Fibonacci numbers, Lucas numbers, continued fractions, suborbital
graphs