Abstract
In this paper, we consider an infinite sub-family of the generalized Petersen graphs P(n, k), for n = 2k + 1 ≥ 3. A. Behzad et al. in [1] gave the upper bound ⌈3n/5⌉ for the domination number of this kind of graphs, where n ≥ 3. They conjectured that the upper bound is sharp. In this paper, we first find a lower bound for the domination number of P(n, k) graphs, where n ≥ 7, and then we give some of the this kind of graphs that their domination numbers achieve the upper bound ⌈3n/5⌉. Also we present their independent domination numbers.
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