Embedded connectivity of ternary n-cubes

•Embedded connectivity of ternary n-cubes was investigated.•The t-embedded vertex connectivity of ternary n-cubes was determined for t≤n−2.•The t-embedded edge connectivity of ternary n-cubes was determined for t≤n−1. Let Gn be an n-dimensional recursive network. A set F⊂V(Gn) (resp. F⊂E(Gn)) is cal...

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Bibliographic Details
Published in:Theoretical computer science 2021-06, Vol.871, p.121-125
Main Author: Yang, Yuxing
Format: Article
Language:English
Subjects:
Connectivity
Embedded connectivity
Fault tolerance
Interconnection network
Ternary n-cubes
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Summary:•Embedded connectivity of ternary n-cubes was investigated.•The t-embedded vertex connectivity of ternary n-cubes was determined for t≤n−2.•The t-embedded edge connectivity of ternary n-cubes was determined for t≤n−1. Let Gn be an n-dimensional recursive network. A set F⊂V(Gn) (resp. F⊂E(Gn)) is called a t-embedded vertex cut (resp. t-embedded edge cut) of Gn if Gn−F is disconnected and each vertex of which lies in a t-dimensional subnetwork of Gn−F. The t-embedded vertex connectivity ζt(Gn) (resp. t-embedded edge connectivity ηt(Gn)) of Gn is the minimum cardinality over all t-embedded vertex cuts (resp. t-embedded edge cuts) in Gn, if any. In this paper, we prove that ζt(Qn3)=2(n−t)3t for 0≤t≤n−2, and ηt(Qn3)=2(n−t)3t for 0≤t≤n−1, where Qn3 is the ternary n-cube.
ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2021.04.016