Structure connectivity and substructure connectivity of bubble-sort star graph networks

Guozhen Zhang and Dajin Wang

Applied Mathematics and Computation, 2019, vol. 363, issue C, -

Abstract: The bubble-sort star graph, denoted BSn, is an interconnection network model for multiprocessor systems, which has attracted considerable interest since its first proposal in 1996 [5]. In this paper, we study the problem of structure/substructure connectivity in bubble-sort star networks. Two basic but important structures, namely path Pi and cycle Ci, are studied. Let T be a connected subgraph of graph G. The T-structure connectivity κ(G; T) of G is the cardinality of a minimum set of subgraphs in G, whose deletion disconnects G and every element in the set is isomorphic to T. The T-substructure connectivity κs(G; T) of G is the cardinality of a minimum set of subgraphs in G, whose deletion disconnects G and every element in the set is isomorphic to a connected subgraph of T. Both T-structure connectivity and T-substructure connectivity are a generalization of the classic notion of node-connectivity. We will prove that for P2k+1, a path on odd nodes (resp. P2k, a path on even nodes), κ(BSn;P2k+1)=κs(BSn;P2k+1)=⌈2n−3k+1⌉ for n ≥ 4 and k+1≤2n−3 (resp. κ(BSn;P2k)=κs(BSn;P2k)=⌈2n−3k⌉ for n ≥ 5 and k≤2n−3). For a cycle on 2k nodes C2k (there are only cycles on even nodes in BSn), κ(BSn;C2k)=κs(BSn;C2k)=⌈2n−3k⌉ for n ≥ 5 and 2≤k≤n−1.

Keywords: Interconnection networks; Structure connectivity; Substructure connectivity; Bubble-sort star graphs; Paths; Cycles (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319306241
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:363:y:2019:i:c:27

DOI: 10.1016/j.amc.2019.124632

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().