Undirected loop networks

Chen, Sheng; Jia, Xingde

doi:10.1002/net.3230230407

Cited by 20 publications

(27 citation statements)

References 4 publications

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“…In this article, we improve the bound for the diameter of graphs in the family of [5], as well as find their exact diameters for a series of dimensions, including k = 4, and theoretically justify and generalize the results that are found by the evolutionary synthesis method. Together with a previous result obtained for multiplicative circulant networks, this enables us to improve the lower bounds for the attainable number of vertices of the circulant networks for all dimensions k ≥ 4.…”

Section: Introductionmentioning

confidence: 90%

“…The family of circulant networks obtained in [5] remains for a long time the best available family in terms of the ratio n/d for all dimensions k ≥ 3. The following theorem was proved in [5]:…”

Section: Introductionmentioning

confidence: 99%

“…where d(i, j) is the length of the shortest path from a vertex i to a vertex j in G. Given positive integers d and k, denote by M (d, k) [5] the maximal possible (attainable) positive integer n such that there exists a set of generators S = (1, s 2 , . .…”

Section: Introductionmentioning

confidence: 99%

“…The extremal family of [5] belongs to the multiplicative circulant networks [3,10,11] with generators being powers of a multiple of 4. This family was also studied by the evolutionary synthesis method of [7].…”

Section: Introductionmentioning

confidence: 99%

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On an extremal family of circulant networks

Монахова

2011

J. Appl. Ind. Math.

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The paper addresses the optimization problem for circulant networks of maximizing the number of vertices given the degree and diameter of a graph. For the graphs in the best available extremal family of circulant networks, we improve the estimate for diameter, which together with previous results for multiplicative circulant networks enables us to improve the lower bounds for the attainable number of vertices of circulant networks of all dimensions k ≥ 4.

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Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On an extremal family of circulant networks

Монахова

2011

J. Appl. Ind. Math.

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“…For 3-dimensional circulants, the algorithm has automatically generated previously unknown descriptions of values of N and S , which correspond to circulant graphs with good extrema1 properties. Also, the EA found a description of the family of graphs described in [6].…”

Section: Resultsmentioning

confidence: 99%

Using evolutionary algorithm for generation of dense families of circulant networks

Monakhov

Монахова

Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600)

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In this paper we consider the combinatorial optimization problem of the search for dense families of circulant networks with a good ratio between the order and diameter for a given degree. In particular, we distinguish the optimal families having the minimum possible diameter for a given degree and order of a graph. This work describes a new way of generation of analytical parametric descriptions of dense families of circulant networks using evolutionary algorithms. We present the families of circulants of degree 4 and 6 obtained by means of evolutionary algorithms. Some of these families of degree 6 improve previously known results.

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Fault-tolerant routings in chordal ring networks

et al. 2000

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This paper studies routing vulnerability in networks modeled by chordal ring graphs. In a chordal ring graph, the vertices are labeled in ℤ2n and each even vertex i is adjacent to the vertices i + a, i + b, i, + c, where a, b, and c are different odd integers. Our study is based on a geometrical representation that associates to the graph a tile which periodically tessellates the plane. Using this approach, we present some previous results on triple‐loop graphs, including an algorithm to calculate the coordinates of a given vertex in the tile. Then, an optimal consistent fault‐tolerant routing of shortest paths is defined for a chordal ring graph with odd diameter and maximum order. This is accomplished by associating to the chordal ring graph a triple‐loop one. When some faulty elements are present in the network, we give a method to obtain central vertices, which are vertices that can be used to reroute any communication affected by the faulty elements. This implies that the diameter of the corresponding surviving route graph is optimum. © 2000 John Wiley & Sons, Inc.

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Undirected loop networks

Cited by 20 publications

References 4 publications

On an extremal family of circulant networks

On an extremal family of circulant networks

Using evolutionary algorithm for generation of dense families of circulant networks

Fault-tolerant routings in chordal ring networks

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