Reliability evaluation for bijection-connected networks based on the super Pk-connectivity

Tzu-Liang Kung

Applied Mathematics and Computation, 2024, vol. 464, issue C

Abstract: With the need for large-scale networks evolving in a variety of fields, such as cloud/edge computing, social networks, privacy protection, etc., the network's robustness against faulty clusters has recently gained more attention. The family of bijection-connected networks includes numerous instances of remarkable network topologies, for example, hypercubes, Möbius cubes, crossed cubes, etc. For a network whose underlying topology is modeled by a graph G, its node-connectivity, κ(G), is a key performance index of network robustness, which is formalized as the total number of nodes in the smallest node-cut of G. Apparently, κ(G) happens to be bounded above by G's minimum degree. A node-cut is trivial if it is nothing but an arbitrary node's neighborhood. Then, G can be r-connected if 1≤r≤κ(G). To say the least, if each smallest node-cut of G is trivial, G is super connected. The super Pk-connectivity is an innovative assessment to quantify the connectedness level of G, where Pk notates a path consisting of k nodes (k≥1). This article aims to investigate the super Pk-connectivity for the bijection-connected networks. With regard to some specific instances, such as hypercubes, locally twisted cubes, etc., a sufficient and necessary condition is established to identify whether they are really super Pk-connected.

Keywords: Connectivity; Cluster-connectivity; Pk-connectivity; Pk-cut; Bijection-connected network (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300323005660
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:464:y:2024:i:c:s0096300323005660

DOI: 10.1016/j.amc.2023.128397

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 ().