The super connectivity of augmented cubes

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 ( 2 n − 1 ) -regular ( 2 n − 1 ) -connected graph ( n ≠ 3 ). This paper determines that the super connectivity of AQ n is 4 n − 8 for n ⩾ 6 and the super edge-con...

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Bibliographic Details
Published in:Information processing letters 2008-04, Vol.106 (2), p.59-63
Main Authors: Ma, Meijie, Liu, Guizhen, Xu, Jun-Ming
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Augmented cube
Computer science
control theory
systems
Computer systems performance. Reliability
Connectivity
Exact sciences and technology
Graph theory
Information retrieval. Graph
Interconnection networks
Miscellaneous
Parallel processing
Software
Studies
Super connectivity
Super edge-connectivity
Theoretical computing
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Summary: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 ( 2 n − 1 ) -regular ( 2 n − 1 ) -connected graph ( n ≠ 3 ). This paper determines that the super connectivity of AQ n is 4 n − 8 for n ⩾ 6 and the super edge-connectivity is 4 n − 4 for n ⩾ 5 . That is, for n ⩾ 6 (respectively, n ⩾ 5 ), at least 4 n − 8 vertices (respectively, 4 n − 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.
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2007.10.005