On suborbital graphs and related continued fractions

Değer, Ali Hikmet; Beşenk, Murat; Güler, Bahadır Özgür

doi:10.1016/j.amc.2011.03.065

Cited by 9 publications

(14 citation statements)

References 4 publications

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“…The G u,N and F u,N suborbital graphs are consisted at these works. 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].…”

Section: Introductionmentioning

confidence: 97%

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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Section: Introductionmentioning

confidence: 97%

The Generating Functions for Special Pringsheim Continued Fractions

Akbaba

Değer

2020

Communications in Advanced Mathematical Sciences

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“… 1991 ); A shortest path in trees of suborbital graphs is a special case of Pringsheim continued fraction (Deger et al. 2011 ); The subgraph can be defined as a new kind of continued fraction and any irrational numbers has a unique expansion (Sarma et al. 2015 ); The set of vertices of some suborbital graphs is strongly connected to the Fibonacci sequence (Akbaş et al.…”

Section: Introductionmentioning

confidence: 99%

“…A shortest path in trees of suborbital graphs is a special case of Pringsheim continued fraction (Deger et al. 2011 );…”

Section: Introductionmentioning

confidence: 99%

Solutions to some congruence equations via suborbital graphs

2016

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“…Elliptic elements do not necessarily correspond to circuits of the same order. On the other hand, it is worth noting that these graphs give some number theoretical results about continued fractions and Fibonacci numbers as in [4,8,17].…”

Section: Introductionmentioning

confidence: 99%

“…Then similar studies were done for related finitely generated groups.The reader is referred to [2][3][4][5]8,9,[11][12][13][14][15][16] for some relevant previous work on suborbital graphs. Firstly, in [3], it was proved that the elliptic elements in Γ 0 (n) correspond to circuits in the subgraph F u,n of the same order and vice versa.…”

Section: Introductionmentioning

confidence: 99%