Graph domination numbers and algorithms for finding them have been investigated for numerous classes of graphs, usually for graphs that have some kind of tree-like structure. By contrast, we study an infinite family of regular graphs, the generalized Petersen graphs G (n). We give two procedures that between them produce both upper and lower bounds for the (ordinary) domination number of G (n), and we conjecture that our upper bound ⌈ 3 n / 5 ⌉ is the exact domination number. To our knowledge this is one of the first classes of regular graphs for which such a procedure has been used to estimate the domination number. © 2007 Elsevier B.V. All rights reserved.
Behzad, A., Behzad, M., & Praeger, C. E. (2008). On the domination number of the generalized Petersen graphs. Discrete Mathematics, 308(4), 603–610. https://doi.org/10.1016/j.disc.2007.03.024