Bound for the k-Fault-Tolerant Power-Domination Number

Autor: Lakshmi Girish, Kanagasabapathi Somasundaram
Jazyk: angličtina
Rok vydání: 2024
Předmět:
Zdroj: Symmetry, Vol 16, Iss 7, p 781 (2024)
Druh dokumentu: article
ISSN: 2073-8994
DOI: 10.3390/sym16070781
Popis: A set S⊆V is referred to as a k-fault-tolerant power-dominating set of a given graph G=(V,E) if the difference S∖F remains a power-dominating set of G for any F⊆S with |F|≤k, where k is an integer with 0≤k<|V|. The lowest cardinality of a k-fault-tolerant power-dominating set is the k-fault-tolerant power-domination number of G, denoted by γPk(G). Generalized Petersen graphs GP(m,k) and generalized cylinders SG are two well-known graph classes. In this paper, we calculate the k-fault-tolerant power-domination number of the generalized Petersen graphs GP(m,1) and GP(m,2). Also, we obtain γPk(G) for the subclasses of cylinders SCm and SBm.
Databáze: Directory of Open Access Journals
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