Abstract

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.

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