Publication

Abstract :

A set 𝑆⊆𝑉S⊆V is referred to as a k-fault-tolerant power-dominating set of a given graph 𝐺=(𝑉,𝐸)G=(V,E) if the difference 𝑆∖𝐹S∖F remains a power-dominating set of G for any 𝐹⊆𝑆F⊆S with |𝐹|≤𝑘|F|≤k, where k is an integer with 0≤𝑘<|𝑉|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 𝛾𝑘𝑃(𝐺)γPk(G). Generalized Petersen graphs 𝐺𝑃(𝑚,𝑘)GP(m,k) and generalized cylinders 𝑆𝐺SG 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)GP(m,1) and 𝐺𝑃(𝑚,2)GP(m,2). Also, we obtain𝛾𝑘𝑃(𝐺)γPk(G) for the subclasses of cylinders 𝑆𝐶𝑚SCm and 𝑆𝐵𝑚SBm.