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

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.18 no.5
• /
• pp.1110-1115
• /
• 2014

The matrix-star and the transposition graphs are considered as star graph variants that have various merits in graph theory such as node symmetry, fault tolerance, recursive scalability, etc. This paper describes an one-to-one mapping algorithm from a matrix-star graph to a transposition graph using adjacent properties in graph theory. The result show that a matrix-star graph $MS_{2,n}$ can be embedded in a transposition graph $T_{2n}$ with dilation n or less and average dilation 2 or less.

• Proceedings of the IEEK Conference
• /
• 1998.10a
• /
• pp.467-470
• /
• 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
• /
• v.9 no.9
• /
• pp.1173-1183
• /
• 2006

Matrix-star, Pancake, and RFM graphs have such a good property of Star graph and a lower network cost than Hypercube. Matrix-star graph has Star graph as a basic module and the node symmetry, the maximum fault tolerance, and the hierarchical decomposition property. Also it is an interconnection network that improves the network cost against Star graph. In this paper, we propose a method to embed among Matrix-star Pancake, and RFM graphs using the edge definition of graphs. We prove that Matrix-star $MS_{2,n}$ can be embedded into Pancake $P_{2n}$ with dilation 4, expansion 1, and $RFM_{n}$ graphs can be embedded into Pancake $P_{n}$ with dilation 2. Also, we show that Matrix-star $MS_{2,n}$ can be embedded into the $RFM_{2n}$ with average dilation 3.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.24 no.4
• /
• pp.430-436
• /
• 2014

Matrix-star and Half-Pancake graphs are modified versions of Star graphs, and has some good characteristics such as node symmetry and fault tolerance. This paper analyzes embedding between Matrix-star and Half-Pancake graphs. As a result, Matrix-star graphs $MS_{2,n}$ can be embedded into Half-Pancake graphs $HP_{2n}$ with dilation 5 and expansion 1. Also, Half Pancake Graphs, $HP_{2n}$ can be embedded into Matrix Star Graphs, $MS_{2,n}$ with the expansion cost, O(n). This result shows that algorithms developed from Star Graphs can be applied at Half Pancake Graphs with additional constant cost because Star Graphs, $S_n$ is a part graph of Matrix Star Graphs, $MS_{2,n}$.