Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

Das, Sajal K.; Öhring, Sabine R.; Banerjee, Amit

doi:10.1155/1995/95759

Cited by 36 publications

(14 citation statements)

References 23 publications

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“…Proof. From Lemma 3.3, we have κ(K m 1 K m 2 · · · K mn ) = n i=1 m i − n, and hence 0 ≤ τ k (C m 1 C m 2 · · · C mn ) ≤ An n-dimensional hyper Petersen network HP n is the product of the well-known Petersen graph and Q n−3 [12], where n ≥ 3 and Q n−3 denotes an (n − 3)-dimensional hypercube. Note that HP 3 is just the Petersen graph.…”

Section: N-dimensional Generalized Hypercube and N-dimensional Hyper mentioning

confidence: 98%

Constructing edge-disjoint Steiner paths in lexicographic product networks

Mao

2017

Applied Mathematics and Computation

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The concept of pedant tree-connectivity was introduced by Hager in 1985. For a graph G = (V, E) and a set S ⊆ V (G) of at least two vertices, an S-Steiner tree or a Steiner tree connecting S (or simply, an S-tree) is a such subgraph T = (V ′ , E ′ ) of G that is a tree with S ⊆ V ′ . For an S-Steiner tree, if the degree of each vertex in S is equal to one, then this tree is called a pedant S-Steiner tree. Two pedant S-Steiner trees T and T ′ are said to be internally disjoint if E(T ) ∩ E(T ′ ) = ∅ and V (T )∩V (T ′ ) = S. For S ⊆ V (G) and |S| ≥ 2, the local pedant tree-connectivity τ G (S) is the maximum number of internally disjoint pedant S-Steiner trees in G. For an integer k with 2 ≤ k ≤ n, pedant tree k-connectivity is defined as τ k (G) = min{τ G (S) | S ⊆ V (G), |S| = k}. In this paper, we prove that for any two connected graphs G and H, τ 3 (G H) ≥ min{3⌊ τ3(G) 2 ⌋, 3⌊ τ3(H) 2 ⌋}. Moreover, the bound is sharp.

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Section: N-dimensional Generalized Hypercube and N-dimensional Hyper mentioning

confidence: 98%

Constructing edge-disjoint Steiner paths in lexicographic product networks

Mao

2017

Applied Mathematics and Computation

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“…An n-dimensional hyper Petersen network HP n is the Cartesian product of Q n−3 and the wellknown Petersen graph [12], where n ≥ 3 and Q n−3 denotes an (n − 3)-dimensional hypercube. The cases n = 3 and 4 of hyper Petersen networks are depicted in Figure 2.…”

Section: N-dimensional Hyper Petersen Networkmentioning

confidence: 99%

Rainbow vertex-connection and graph products

Mao

Yanling

Wang

et al. 2015

International Journal of Computer Mathematics

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A vertex-coloured graph G is said to be rainbow vertex-connected if every two vertices of G are connected by a path whose internal vertices have distinct colours, such a path is called a rainbow path. The rainbow vertex-connection number of a connected graph G, denoted by rvc(G), is the smallest number of colours that are needed in order to make G rainbow vertex-connected. In this paper, we study the rainbow vertexconnection number on the lexicographical, strong, Cartesian and direct product and present several upper bounds for these products of graphs. The rainbow vertex-connection number of some product networks is also investigated in this paper.

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“…A n-dimensional hyper-Petersen network [Das et al 1995], denoted by HP" for n > 3, is defined as HPn = P x Q"_3, where P is a Petersen graph. An HP" is n-connected and n-regular and has 10 * 2"-^ nodes.…”

Section: Strong Diagnosability For Comparison-based Diagnosismentioning

confidence: 99%

A survey of comparison-based system-level diagnosis

2011

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ParanáThe growing complexity and dependability requirements of hardware, software, emd networks demand efficient techniques for discovering disruptive behavior in those systems. Comparison-based diagnosis is a realistic approach to detect faulty units based on the outputs of tasks executed by system units. This survey integrates the vast amount of research efforts that have been produced in this field, from the earliest theoretical models to new promising applications. Key results also include the quantitative evaluation of a relevant reliability metric-the diagnosability-of several popular interconnection network topologies. Relevant diagnosis algorithms are also described. The survey aims at clarifying and uncovering the potential of this technology, which can be applied to improve the dependability of diverse complex computer systems. . 2011. A survey of comparison-based system-level diagnosis.

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Embeddings into Hyper Petersen Networks: YetAnother Hypercube‐Like Interconnection Topology

Cited by 36 publications

References 23 publications

Constructing edge-disjoint Steiner paths in lexicographic product networks

Constructing edge-disjoint Steiner paths in lexicographic product networks

Rainbow vertex-connection and graph products

A survey of comparison-based system-level diagnosis

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