Fault-tolerant basis of generalized fat trees and perfect binary tree derived architectures

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F24%3A00585137" target="_blank" >RIV/67985807:_____/24:00585137 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1007/s11227-024-06053-5" target="_blank" >https://doi.org/10.1007/s11227-024-06053-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11227-024-06053-5" target="_blank" >10.1007/s11227-024-06053-5</a>

Result language

angličtina

Original language name

Fault-tolerant basis of generalized fat trees and perfect binary tree derived architectures

Original language description

The ability to uniquely identify all nodes in a network based on network distances has proven to be highly beneficial despite the computational challenges involved in discovering minimal resolving sets within an interconnection network. A subset $R$ of vertices of a graph $G$ is referred to as a resolving set of the graph if each node can be uniquely identified by its distance code with respect to $R$, with its minimal cardinality defining the metric dimension of $G$. Similarly, a resolving set $F subseteq V$ is designated as a fault-tolerant resolving set if $F setminus {s}$ serves as a resolving set for each $s in F$. The minimum cardinality of $F$ represents the fault-tolerant metric dimension of $G$. Although determining the precise metric dimension of a given graph remains challenging, various effective techniques and meaningful constraints have been developed for different graph families. However, no notable technique has been developed to find fault-tolerant metric dimension of a given graph. Recently, Prabhu et al. have shown that each twin vertex of $G$ belongs to every fault-tolerant resolving set of $G$. Consequently, the fault-tolerant metric dimension is equal to the order of the graph $G$ if and only if each vertex of $G$ is a twin vertex, a characterization proved in [Appl. Math. Comput. textbf{420} (2022) 126897] corrects a wrong characterization in the literature. It is also interesting to note from the above literature correction that the twin vertices are necessary to form the fault-tolerant resolving set, but determining whether they are sufficient is challenging. Evidence of this context is also discussed in this paper through the amalgamation of perfect binary trees. This article focuses on determining the exact value of the fault-tolerant metric dimension of generalized fat trees. For the amalgamation of perfect binary trees, both the metric dimension and fault-tolerant metric dimension were precisely found.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Supercomputing

ISSN

0920-8542

e-ISSN

1573-0484

Volume of the periodical

80

Issue of the periodical within the volume

July

Country of publishing house

DE - GERMANY

Number of pages

16

Pages from-to

15783-15798

UT code for WoS article

001197630900005

EID of the result in the Scopus database

2-s2.0-85189295638