• Proceedings of the IEEK Conference
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• 2002.06c
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• pp.169-172
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• 2002

In this paper, we consider the problem of embedding Fibonacci linear array, Fibonacci mesh, Fibonacci tree into Fibonacci circulants and between Fibonacci cubes and Fibonacci circulants. We show that the Fibonacci linear array of order n , Ln is a subgraph of the Fibonacci circulants of order n , En with En◎ Ln,n≥0 , the Fibonacci mesh of order (nt,n2), M(n,.nT)with S2n.1 f( M(n.れ)닌 M(n.1.n.1)), 52れ 늰( M(n.n.1)띤 M(H.n-1)) and the Fibonacci tree-lof order n, FT/sub n/ with ∑/sub n+3/⊇ FTn , n≥0, the Fibonacci tree-ll of order n , Tれ with ∑/sub n/⊇ Tn Fu퍼hermore, 낀e show that the Fibonacci cubes of order n , rn is subgraph of the Fibonacci circulants of order n , En and inversely rn can be embedded into En with expansion 1, dilation n -2 and congestion.

• The KIPS Transactions:PartA
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• v.14A no.4
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• pp.249-254
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• 2007

In this paper, we consider the embedding problem of postorder Fibonacci circulant. We show that Fibonacci linear array, Fibonacci mesh, Fibonacci tree, Fibonacci cubes and Hypercube are a subgraph of postorder Fibonacci circulant.

• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.1-84
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• 2017

In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where p is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, m and derive certain interesting properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.731-734
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• 2000

We present a novel graph labeling problem called Fibonacci edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be (3m+2)-th Fibonacci numbers. We show that every Fibonacci tree can be labeled Fibonacci edge labeling. The labelings on the Fibonacci trees are applied to their embeddings into Fibonacci Circulants.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.231-240
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• 2005

We examine the Fibonacci length of certain centro-polyhedral groups and show that in some cases the lengths depend on tribonacci sequences. Further we obtain specific examples of infinite families of three-generator groups with constant, linear and (3-step) Wall number dependent Fibonacci lengths.

• Honam Mathematical Journal
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• v.38 no.4
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• pp.675-683
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• 2016

We give the representation of Fibonacci quaternions for convenient calculus. We research the corresponding properties of Fibonacci quaternions and some examples of a function with values in modified Fibonacci quaternions.

• Proceedings of the IEEK Conference
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• 2004.06a
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• pp.163-166
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• 2004

In this paper, we consider the embedding problem of postorder Fibonacci circulants. We show that Fibonacci cubes and Hypercube are a subgraph of postorder Fibonacci circulants. And the postorder Fibonacci circulants of order n can be embedded into the Fibonacci cubes of order n with expansion 1, dilation n-2 and congestion O (n-1), the Hypercube of order n-2 with expansion $\frac{f_n}{2^{n-2}}$, dilation n-2 and congestion O(n-2).

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.1-16
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• 2016

The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the modified k-Fibonacci-like sequence and prove Binet's formula for this sequence and then use it to introduce and prove the Catalan, Cassini, and d'Ocagne identities for the modified k-Fibonacci-like sequence. Also, the ordinary generating function of this sequence is stated.

• Proceedings of the Korea Information Processing Society Conference
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• 2006.05a
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• pp.743-746
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• 2006

In this paper, we propose and analyze a new parallel computer topology, called the Fibonacci posterorder circulants. It connects ${\Large f}_x,\;n{\geq}2$ processing nodes, same the number of nodes used in a comparable Fibonacci cube. Yet its diameter is only ${\lfloor}\frac{n}{3}{\rfloor}$ almost one third that of the Fibonacci cube. Fibonacci cube is asymmetric, but it is a regular and symmetric static interconnection networks for large-scale, loosely coupled systems. It includes scalability and Fibonacci cube as a spanning subgraph.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.47-54
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• 2024

In this paper, we investigate the distribution of the zeros of the Bernoulli-Fibonacci polynomials by using computer.