On the power domination number of the generalized Petersen graphs

Power Domination in Graphs

“…The case of generalized Petersen graphs was considered by both Barrera and Ferrero in [4] and by Xu and Kang in [31]. In [4], they suggest a more general study on Cayley graphs as a continuation of this study.…”

Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

“…In the recently published literature, various properties of GP (n, k) have been investigated: minimum span of L(2, 1)-labeling [1], minimum vertex cover [4], metric dimension [2,27], strong metric dimension [18], decycling number [13], component connectivity [10], acyclic 3-coloring [34], crossing numbers [25], independence number [11], and others. Some recent works dealing with variants of the domination numbers in the generalized Petersen graphs are: domination number [3,12,26], domatic number, total domatic number, and k-ply domatic number [33], efficient domination number [17], power domination number [32], 2-rainbow domination [5,31], and others.…”

Generalized power domination in claw-free regular graphs

“…The exact values for the power domination numbers were determined for various products of graphs in [8,9] and some important graphs in [19,24]. Bounds for the power domination numbers of connected graphs and of claw-free cubic graphs were given in [18], for planar or outerplanar graphs with bounded diameter in [23], for Knödel graphs in [19], and for generalized Petersen graphs in [21,24]. The Nordhaus-Gaddum problems for power domination were investigated in [4].…”