Vertices of paths of minimal lengths on suborbital graphs

Değer, Ali Hikmet

doi:10.2298/fil1704913d

Cited by 5 publications

(10 citation statements)

References 6 publications

(14 reference statements)

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“…Theorem 2.1. [4] If (u, N) = 1, then exist an integer t such that u 2 + tu + 1 ≡ 0 (mod N), for t ≥ 2.…”

Section: Resultsmentioning

confidence: 99%

“…In [3] and [8], the results are extended. The definition of minimal length path for F u,N suborbital graphs is given by Deger in [4]. In [4], it has been showed that; there is a integer t, which provides u 2 + tu + 1 ≡ 0 (mod N) congruence equation for F u,N suborbital graphs.…”

Section: Introductionmentioning

confidence: 99%

“…The definition of minimal length path for F u,N suborbital graphs is given by Deger in [4]. In [4], it has been showed that; there is a integer t, which provides u 2 + tu + 1 ≡ 0 (mod N) congruence equation for F u,N suborbital graphs. By using integer t, the vertices on the minimal length path of F u,N suborbital graphs are consisted with Pringsheim continued fractions, according to edge conditions of F u,N suborbital graphs [3].…”

Section: Introductionmentioning

confidence: 99%

“…By using integer t, the vertices on the minimal length path of F u,N suborbital graphs are consisted with Pringsheim continued fractions, according to edge conditions of F u,N suborbital graphs [3]. When t = 3, the continued fractions give the even term index Fibonacci numbers [4].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Generating Functions for Special Pringsheim Continued Fractions

Akbaba

Değer

2020

Communications in Advanced Mathematical Sciences

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In previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs F u,N were investigated. Then, for special vertices, the relations between these vertices and Fibonacci numbers were examined. On the other hand, Koshy studied relation between recurrence relations of Fibonacci numbers, Pell numbers and generating functions. In this work, it is showed that every vertex on the path of minimal length of suborbital graph F u,N has a Pringsheim continued fraction. Then, by Koshy's motivation, the generating function of the recurrence relation of these pringsheim continued fractions are examined.

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“…Theorem 2.1. [4] If (u, N) = 1, then exist an integer t such that u 2 + tu + 1 ≡ 0 (mod N), for t ≥ 2.…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Generating Functions for Special Pringsheim Continued Fractions

Akbaba

Değer

2020

Communications in Advanced Mathematical Sciences

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“…Elliptic elements and elliptic circuits are investigated in [6]. In [7], it is shown that each vertex in the suborbital graph F u,N has a continued fraction structure for (u, N ) = 1 and u ≤ N and investigated the vertices on path with minimal lengths. Suborbital graphs are studied for invariant groups in [8].…”

Section: Introductionmentioning

confidence: 99%

Vertices of Suborbital Graph $F_{u,N}$ under Lorentz Matrix Multiplication

SCIENCES

Değer

2022

Journal of New Theory

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In this study, suborbital graphs, $G_{u,N}$ and $F_{u,N}$ are examined. Modular group $\Gamma$ and its act on $\widehat{\mathbb{Q}}$ are studied. Lorentz matrix that gives the vertices obtained under the classical matrix multiplication in the suborbital graph $F_{u,N}$ is analysed with the Lorentz matrix multiplication. Lorentz matrix written as Möbius transform is normalized and the type of the transform is researched. Moreover, a different element of Modular group $\Gamma$ is scrutinized. The vertices on the path starting with $\infty$ are obtained under this element and the Lorentz matrix multiplication. For this path, it is shown that the vertices obtained in $F_{u,N}$ under the Lorentz matrix multiplication with the Lorentz matrix satisfied the farthest vertex condition for the previous vertex.

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Some special values of vertices of trees on the suborbital graphs

Değer

Akbaba

2018

AIP Conference Proceedings

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Vertices of paths of minimal lengths on suborbital graphs

Cited by 5 publications

References 6 publications

The Generating Functions for Special Pringsheim Continued Fractions

The Generating Functions for Special Pringsheim Continued Fractions

Vertices of Suborbital Graph $F_{u,N}$ under Lorentz Matrix Multiplication

Some special values of vertices of trees on the suborbital graphs

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