Some special values of vertices of trees on the suborbital graphs

Değer, Ali Hikmet; Akbaba, Ümmügülsün

doi:10.1063/1.5020462

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Suborbital Graphs1

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2020

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“…By this relation, we can write r s ≈ x y ⇐⇒ ry − sx ≡ 0mod(N). For details, see [8], [9], [3]. These ideas firstly were used by Sims [2], and got important in books by Tsukuzu [10], Biggs and White [11] with applying to finite groups.…”

Section: Suborbital Graphsmentioning

confidence: 99%

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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