• 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).

• 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.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.471-474
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• 1998

In this paper, we consider the problem of optimal broadcasting in recursive circulants under multi-port communication model. Recursive circulant G(N, d) that is defined to be a circulant graph with N vertices and jumps of powers of d is a useful interconnection network from the viewpoint of network metrices. Our model assumes that a processor can transmit a message to $\alpha$ neighboring processors simultaneously where $\alpha$ is two or three. For the broadcasting problem, we introduce 3-trees and 4-trees. And then we show that 3-trees and 4-trees are minimum broadcast trees in 2-port model and 3-port model. Using the above results, we show that recursive circulants g(2m, 2) have optimum broadcasting time in 2-port model and 3-port model.

• The KIPS Transactions:PartA
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• v.15A no.1
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• pp.27-34
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• 2008

In this paper, We propose a new parallel computer topology, called the Postorder Fibonacci Circulants and analyze its properties. It is compared with Fibonacci cubes, when its number of nodes is kept the same of comparable one. Its diameter is improved from n-2 to $[\frac{n}{3}]$ and its topology is changed from asymmetric to symmetric. It includes Fibonacci cube as a spanning graph.

• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.201-217
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• 2019

Ricci curvature for locally finite graphs, as proposed by Lin, Lu and Yau, provides a useful isomorphism invariant. A Matching Condition was introduced as a key tool for computation of this Ricci curvature. The scope of the Matching Condition is quite broad, but it does not cover all cases. Thus the current paper introduces extended versions of the Matching Condition, and applies them to the computation of the Ricci curvature of a class of circulants determined by certain number-theoretic data. The classical Matching Condition is also applied to determine the Ricci curvature for other families of circulants, along with Cayley graphs of abelian groups that are generated by the complements of (unions of) subgroups.

• Proceedings of the IEEK Conference
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• 2004.06a
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• pp.91-94
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• 2004

In this paper, we propose a new parallel computer topology, called the postorder Fibonacci circulants and analyze its properties. It is compared with Fibonacci cubes, when its number of nodes and its degree is kept the same of comparable one. Its diameter is improved from n-2 to [$\frac{n}{3}$] and a its topology is changed from asymmetric to symmetric. It includes Fibonacci cube as a spanning tree.

• 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 KIISE:Computer Systems and Theory
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• v.29 no.9
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• pp.493-502
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• 2002

The connectivity and edge-connectivity have been the prime deterministic measure of fault tolerance in multicomputer networks. These parameters have a problem that they do not differentiate the different types of disconnected graphs which result from removing the disconnecting vertices or disconnecting edges. To compensate for this shortcoming, one can utilize generalized measures of connectedness such as superconnectivity, toughness, scattering number, vertex-integrity, binding number, and restricted connectivity. In this paper, we analyze such deterministic measures of fault tolerance in recursive circulants and hypercubes, and compare them in terms of fault tolerance.

• Kyungpook Mathematical Journal
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• v.25 no.1
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• pp.71-75
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• 1985

• Journal of applied mathematics & informatics
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• v.2 no.2
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• pp.3-12
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• 1995

Evaluation of permanents of some(0,1) circulants is known to be of major importance for designers of certain speech scrambling systems. In this paper we gicve a lower bound for the number of scaram-bling patterns we deal with by minimizing the permanent function over some matrix polyhedra.