The structure fault tolerance of arrangement graphs

Guozhen Zhang and Dajin Wang

Applied Mathematics and Computation, 2021, vol. 400, issue C

Abstract: The arrangement graph An,k is a prominent underlying topology for multi-processor/multi-computer networks. In this paper, we study the structure fault tolerance of An,k for two structures of interest and significance - the m-leaves starSm, and the m-leaves 2-step starT2m. Let G be a connected graph and H a connected subgraph of G. The H-structure connectivityκ(G;H) (resp. H-substructure connectivityκs(G;H)) of G is the cardinality of a minimum collection F={H1,H2,…,Ht}, such that for each and every 1≤i≤t,Hi⊆G and Hi is isomorphic to H (resp. isomorphic to a connected subgraph of H), and the removal of F disconnects G. In this paper, we will determine κ(An,k;H) and κs(An,k;H) for H∈{Sm,T2m}. Our result adds to the many known, desirable properties of An,k, providing more perspectives when considering its candidacy as an interconnection network for multiprocessor systems.

Keywords: Interconnection networks; Structure connectivity; Substructure connectivity; Arrangement graphs; Stars; 2-step stars (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:400:y:2021:i:c:s0096300321000874

DOI: 10.1016/j.amc.2021.126039

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