• The Transactions of the Korea Information Processing Society
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• v.6 no.3
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• pp.571-579
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• 1999

A Macro-Star graph which has a star graph as a basic module has node symmetry, maximum fault tolerance, and hierarchical decomposition property. And, it is an interconnection network which improves a network cost against a star graph. A matrix star graph also has such good properties of a Macro-Star graph and is an interconnection network which has a lower network cost than a Maco-Star graph. In this paper, we propose a method to embed between a Macro-Star graph and a matrix star graph. We show that a Macro-Star graph MS(k, n) can be embedded into a matrix star graph MS\ulcorner with dilation 2. In addition, we show that a matrix star graph MS\ulcorner can be embedded into a Macro-Star graph MS(k,n+1) with dilation 4 and average dilation 3 or less as well. This result means that several algorithms developed in a star graph can be simulated in a matrix star graph with constant cost.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.467-470
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• 1998

In this paper, we propose a matrix star graph which improves the network cost of the well-known star grah as an interconnection network. We analyze its characteristics in terms of the network parameters, such as degree, scalability, routing, and diameter. The proposed matrix star graph MS2,n has the half degrees of a star graph S2n with the same number of nodes and is an interconnection network with the properties of node symmetry, maximum fault tolerance, and recursive structure. In network cost, a matrix star graph MS2,n and a star graph S2n are about 3.5n2 and 6n2 respectively which means that the former has a better value by a certain constant than the latter has.

• Journal of Korea Multimedia Society
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• v.17 no.6
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• pp.725-732
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• 2014

The Pancake graph is node symmetric and useful interconnection network in the field of data sorting algorithm. The Half Pancake graph is a new interconnection network that reduces the degree of the Pancake graph by approximately half and improves the network cost of the Pancake graph. In this paper, we analyze topological properties of the Half Pancake graph $HP_n$. Fist, we prove that $HP_n$ has maximally fault tolerance and recursive scalability. In addition, we show that in $HP_n$, there are isomorphic graphs of low-dimensional $HP_n$. Also, we propose that the Bubblesort $B_n$ can be embedded into Half Pancake $HP_n$ with dilation 5, expansion 1. These results mean that various algorithms designed for the Pancake graph and the Bubble sort graph can be executed on $HP_n$ efficiently.

• The KIPS Transactions:PartA
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• v.11A no.5
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• pp.341-346
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• 2004

Recently A Hyper-Star Graph HS(m, k) has been introduced as a new interconnection network of new topology for parallel processing. Hyper-Star Graph has properties of hypercube and star graph, further improve the network cost of a hypercube with the same number of nodes. In this paper, we show that Hyper-Star Graph HS(m, k) is subgraph of hypercube. And we also show that regular graph, Hyper-Star Graph HS(2n, n) is node-symmetric by introduced mapping algorithm. In addition, we introduce an efficient one-to-all broadcasting scheme - takes 2n-1 times - in Hyper-Star Graph HS(2n, n) based on a spanning tree with minimum height.

• The Transactions of the Korea Information Processing Society
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• v.5 no.10
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• pp.2615-2626
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• 1998

In this paper, we propose a new interconnection network called RFM graph, whichis the merger of the directed rotator and Faber-Moore graph, and analyze fault tolerance, routing algorithm node disjoint cycles and broadcasting algorithm. We also describe methods to embed star graph, 2 dimesional torus and bubblesort graph into RFM graph with unit expasion and dilation 2.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.42 no.1
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• pp.27-34
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• 2005

In this paper, we propose the Q-edge labeling method related to the graph embedding problem in binomial trees. This result is able to design a new reliable interconnection networks with maximum connectivity using Q-edge labels as jump sequence of circulant graph. The circulant graph is a generalization of Harary graph which is a solution of the optimal problem to design a maximum connectivity graph consists of n vertices End e edgies. And this topology has optimal broadcasting because of having binomial trees as spanning tree.

• The Journal of Korean Association of Computer Education
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• v.17 no.2
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• pp.115-124
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• 2014

Hypercube and star graph are widely known as interconnection network. The embedding of an interconnection network is a mapping of a network G into other network H. The possibility of embedding interconnection network G into H with a low cost, has an advantage of efficient algorithms usage in network H, which was developed in network G. In this paper, we provide an embedding algorithm between HCN and HON. HCN(n,n) can be embedded into HON($C_{n+1},C_{n+1}$) with dilation 3 and HON($C_d,C_d$) can be embedded into HCN(2d-1,2d-1) with dilation O(d). Also, star graph can be embedded to half pancake's value of dilation 11, expansion 1, and average dilation 8. Thus, the result means that various algorithms designed for HCN and Star graph can be efficiently executed on HON and half pancake, respectively.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.21 no.7
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• pp.1327-1334
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• 2017

The Bubble sort graph is node symmetric, and can be used in the data sorting algorithm. In this research we propose and analyze that Half Bubble sort graph that improved the network cost of Bubble sort graph. The Half Bubble sort graph's number of node is n!, and its degree is ${\lfloor}n/2{\rfloor}+1$. The Half Bubble sort graph's degree is $${\sim_=}0.5$$ times of the Bubble sort, and diameter is $${\sim_=}0.9$$ times of the Bubble sort. The network cost of the Bubble sort graph is $${\sim_=}0.5n^3$$, and the network cost of the half Bubble sort graph is $${\sim_=}0.2n^3$$. We have proved that half bubble sort graph is a sub graph of the bubble sort graph. In addition, we proposed a routing algorithm and analyzed the diameter. Finally, network cost is compared with the bubble sort graph.

• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.205-225
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• 2022

In this paper, we derive analytical closed results for the first (a, b)-KA index, the Sombor index, the modified Sombor index, the first reduced (a, b)-KA index, the reduced Sombor index, the reduced modified Sombor index, the second reduced (a, b)-KA index and the mean Sombor index mSO_α for the OTIS biswapped networks by considering basis graphs as path, wheel graph, complete bipartite graph and r-regular graphs. Network theory plays a significant role in electronic and electrical engineering, such as signal processing, networking, communication theory, and so on. A topological index (TI) is a real number associated with graph networks that correlates chemical networks with a variety of physical and chemical properties as well as chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has recently received increased interest due to its potential uses in parallel and distributed systems.

• Journal of Korea Multimedia Society
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• v.17 no.6
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• pp.716-724
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• 2014

The pancake graph is node symmetric and is utilized on the data sorting algorithm. We propose a new half pancake graph that improve pancake graph's network cost. The half pancake degree is approximately half of pancakes degree and diameter is 3n+4. The pancake graph's network cost is $O(1.64n^2)$ and half pancake's is $O(1.5n^2)$. Additionally half pancake graph is sub graph of pancake graph. As this result, The several algorithms developed in pancake graph has the advantage of leverage on the pancake by adding constant cost.