Augmented cubes

Choudum, S. A.; Sunitha, V.

doi:10.1002/net.10033

Cited by 146 publications

(96 citation statements)

References 24 publications

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“…For the augmented cube AQ n proposed by Choudum and Sunitha [15], Xu and Xu [66] showed that ξ(AQ n ) = 2 n 9 + (−1) n+1 9 + n2 n 3 − 2 n + 1,…”

Section: For a Directed Cyclementioning

confidence: 99%

The forwarding indices of graphs - a survey

2013

OpMath

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Abstract. A routing R of a connected graph G of order n is a collection of n(n − 1) simple paths connecting every ordered pair of vertices of G. The vertex-forwarding index ξ(G, R) of G with respect to a routing R is defined as the maximum number of paths in R passing through any vertex of G. The vertex-forwarding index ξ(G) of G is defined as the minimum ξ(G, R) over all routings R of G. Similarly, the edge-forwarding index π(G, R) of G with respect to a routing R is the maximum number of paths in R passing through any edge of G. The edge-forwarding index π(G) of G is the minimum π(G, R) over all routings R of G. The vertex-forwarding index or the edge-forwarding index corresponds to the maximum load of the graph. Therefore, it is important to find routings minimizing these indices and thus has received much research attention for over twenty years. This paper surveys some known results on these forwarding indices, further research problems and several conjectures, also states some difficulty and relations to other topics in graph theory.

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“…For the augmented cube AQ n proposed by Choudum and Sunitha [15], Xu and Xu [66] showed that ξ(AQ n ) = 2 n 9 + (−1) n+1 9 + n2 n 3 − 2 n + 1,…”

Section: For a Directed Cyclementioning

confidence: 99%

The forwarding indices of graphs - a survey

2013

OpMath

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“…It is well known that the hypercube is one of the most popular interconnection networks for parallel computer/communication system. As an enhancement on the hypercube Q n , the augmented cube AQ n , proposed by Choudum and Sunitha [2], not only retains some of the favorable properties of Q n but also possesses some embedding properties that Q n does not (see, for example, [6,9]). In this paper, we prove that κ (AQ n ) = 4n−8 for n 6 and λ (AQ n ) = 4n − 4 for n 5.…”

Section: Networkmentioning

confidence: 99%

“…It has been shown that AQ n (n = 3) is a (2n − 1)-regular (2n − 1)-connected graph in [2]. The following two properties are derived directly from Definition 2.…”

Section: Definitionmentioning

confidence: 99%

The super connectivity of augmented cubes

Liu

2008

Information Processing Letters

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The augmented cube AQ n , proposed by Choudum and Sunitha [S.A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71-84], is a (2n − 1)-regular (2n − 1)-connected graph (n = 3). This paper determines that the super connectivity of AQ n is 4n − 8 for n 6 and the super edge-connectivity is 4n − 4 for n 5. That is, for n 6 (respectively, n 5), at least 4n − 8 vertices (respectively, 4n − 4 edges) of AQ n are removed to get a disconnected graph that contains no isolated vertices. When the augmented cube is used to model the topological structure of a large-scale parallel processing system, these results can provide more accurate measurements for reliability and fault tolerance of the system.

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“…However, a multitude of different interconnection networks have been devised and developed in a continuing search for improved performance, with many of these networks having hypercubes at their roots. Amongst these generalisations of hypercubes are k-ary n-cubes [14], augmented cubes [12], cube-connected cycles [26], twisted cubes [19], twisted n-cubes [18], crossed cubes [16], folded hypercubes [17], Mcubes [30], Möbius cubes [13], generalised twisted cubes [11], shuffle cubes [24], k-skip enhanced cubes [31], twisted hypercubes [22], supercubes [29], and Fibonacci cubes [20].…”

Section: Introductionmentioning

confidence: 99%

“…Another generalisation of hypercubes are augmented cubes, recently proposed by Choudum and Sunitha [12] as improvements over hypercubes. Hypercubes and augmented cubes (of the same dimensions) have the same sets of vertices.…”

Section: Introductionmentioning

confidence: 99%

Augmented k-ary n-cubes

Xiang

Stewart

2011

Information Sciences

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. We define an interconnection network AQ n,k which we call the augmented kary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQ n,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube AQ n,k : is a Cayley graph, and so is vertex-symmetric, but not edge-symmetric unless n = 2; has connectivity 4n−2 and wide-diameter at most max{(n−1)k−(n−2), k+7}; has diameter ⌊ k 3⌉, when n = 2; and has diameter at most k 4 (n + 1), for n ≥ 3 and k even, and at most k 4 (n + 1) + n 4 , for n ≥ 3 and k odd.

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Augmented cubes

Cited by 146 publications

References 24 publications

The forwarding indices of graphs - a survey

The forwarding indices of graphs - a survey

The super connectivity of augmented cubes

Augmented k-ary n-cubes

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