4.4 Article

On extra connectivity and extra edge-connectivity of balanced hypercubes

Journal

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 94, Issue 4, Pages 813-820

Publisher

TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2016.1148813

Keywords

Interconnection networks; the balanced hypercube; reliability; 2-extra edge-connectivity; 2-extra connectivity

Funding

  1. NSFC [11201208, 11201201]

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The balanced hypercube BHn, as a new variation of the hypercube, possesses many attractive properties such that the hypercube dose not have. Given a connected graph G and a non- negative integer g, the g-extra connectivity (resp. g- extra edge-connectivity) of G, denoted byk(g)(G) (resp.lambda(g)( G)), is the minimal cardinality of a set of vertices (resp. edges) of G, if exists, whose deletion disconnects G and each remaining component contains more than g vertices. In this paper, we show that the 2-extra connectivity of BHn is 4n-4 and 2-extra edge- connectivity of BHn is 6n-4 for n >= 2. Also, we determine 3-extra connectivity of BHn for n >= 2.

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