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Survey on path and cycle embedding in some networks

A combination of energy method and spectral analysis for study of equations of gas motion

Singularities of symplectic and Lagrangian mean curvature flows

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Survey on path and cycle embedding in some networks

Content Provider	Springer Nature Link
Author	Xu, Jun Ming Ma, Meijie
Copyright Year	2009
Abstract	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.
Starting Page	217
Ending Page	252
Page Count	36
File Format	PDF
ISSN	16733452
Journal	Frontiers of Mathematics in China
Volume Number	4
Issue Number	2
e-ISSN	16733576
Language	English
Publisher	SP Higher Education Press
Publisher Date	2009-03-11
Publisher Institution	Chinese Universities
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	Cycle path pancyclicity hamiltonicity panconnectivity fault-tolerance hypercube-like network embedding Paths and cycles Network models, deterministic Mathematics
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model

Fault-Tolerant Path-Embedding of Twisted Hypercube-Like Networks (THLNs)

Edge-pancyclicity and Edge-hamiltonian of Augmented Hypercube

Panconnectivity and pancyclicity of Hypercube-Like Interconnection Networks with faulty elements (2016)

Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements (2006)

Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements (2016)

Cycle and Path Embedding on 5-ary N-cubes

Fault-tolerant cycle embedding in restricted hypercube-like networks with more faulty nodes

Survey on path and cycle embedding in some networks

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Fault-tolerant panconnectivity of augmented cubes

Pancyclicity of Restricted Hypercube-Like Networks under the Conditional Fault Model

Fault-Tolerant Path-Embedding of Twisted Hypercube-Like Networks (THLNs)

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Panconnectivity and pancyclicity of Hypercube-Like Interconnection Networks with faulty elements (2016)

Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements (2006)

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