On the arrangement graph

Chiang, Wei-Kuo; Chen, Rong-Jaye

doi:10.1016/s0020-0190(98)00052-0

Cited by 60 publications

(22 citation statements)

References 3 publications

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“…, k} and p j ϭ q j for all j i. It has been shown respectively in [8] and [6] that the arrangement graphs A r,rϪ1 and A r,rϪ2 are isomorphic to the r-dimensional star graph S r and the rdimensional alternating group graph AG r , respectively.…”

Section: Discussionmentioning

confidence: 99%

Panconnectivity, fault‐tolerant hamiltonicity and hamiltonian‐connectivity in alternating group graphs

et al. 2004

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Section: Discussionmentioning

confidence: 99%

Panconnectivity, fault‐tolerant hamiltonicity and hamiltonian‐connectivity in alternating group graphs

et al. 2004

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“…Moreover, is isomorphic to the complete graph , and is isomorphic to the -dimensional star graph . Chiang and Chen [4] showed that is isomorphic to the -alternating group graph . Recent years have witnessed the continued interest in the research of arrangement graphs [8], [9], [13], [17], [19], [24], [25].…”

Section: Index Terms-arrangement Graph Inclusion-exclusion Prinmentioning

confidence: 99%

The Reliability of Subgraphs in the Arrangement Graph

Lin

Zhou

et al. 2015

IEEE Trans. Rel.

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As the size of a multiprocessor computer system grows, the probability of having faulty (i.e., malfunctioning or failing) processors in the system increases. It is then important to quantify how the faults collectively affect the entire system. The reliability of subsystems in a system, defined as the probability that a fault-free subsystem of a certain size still exists when the system has faults, is a measure for the faults' effect on the whole system. It can be used as an indicator of system health. In this paper, we will present two schemes to calculate the reliability of an -subgraph in the -Arrangement Graph , an extensively studied interconnection network proposed for multiprocessor computers. The first scheme will use a probability fault model and the Principle of Inclusion-Exclusion to establish an upper-bound of the reliability, by taking into account the intersection of not more than three subgraphs. The second scheme uses basically the same idea, but completely neglects the intersection among subgraphs to calculate an approximate reliability. The results of the two schemes are compared, and are shown to be in good agreement, especially as the single-node reliability goes low.

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“…Moreover, AG n , which belongs to the class of Cayley graphs, has been shown to be vertex-transitive, edge-transitive, maximal connectivity, and has a small diameter and average distance. Furthermore, Chiang and Chen [35] showed that AG n is isomorphic to the (n, n−2)-arrangement graph A n,n−2 .…”

Section: Alternating Group Graphsmentioning

confidence: 99%

Survey on path and cycle embedding in some networks

2009

Front. Math. China

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To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic problem. A stronger concept than the pancylicity is the panconnectivity. A graph of order n is said to be panconnected if for any pair of different vertices x and y with distance d there exist xy-paths of every length from d to n. The pancyclicity or the panconnectivity is an important property to determine if the topology of a network is suitable for some applications where mapping cycles or paths of any length into the topology of the network is required. The pancyclicity and the panconnectivity of interconnection networks have attracted much research interest in recent years. A large amount of related work appeared in the literature, with some repetitions. The purpose of this paper is to give a survey of the results related to these topics for the hypercube and some hypercube-like networks.

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On the arrangement graph

Cited by 60 publications

References 3 publications

Panconnectivity, fault‐tolerant hamiltonicity and hamiltonian‐connectivity in alternating group graphs

Panconnectivity, fault‐tolerant hamiltonicity and hamiltonian‐connectivity in alternating group graphs

The Reliability of Subgraphs in the Arrangement Graph

Survey on path and cycle embedding in some networks

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