On the domination number of generalized Petersen graphs

Let n and k be integers such that 3≤2k+1≤n. The generalized Petersen graph GP(n,k)=(V,E) is the graph with V={u1,u2,…,un}∪{v1,v2,…,vn} and E={uiui+1,uivi,vivi+k:1≤i≤n}, where addition is in modulo n. A subset D⊆V is a dominating set of GP(n,k) if for each v∈V∖D there is a vertex u∈D adjacent to v. The minimum cardinality of a dominating set of GP(n,k) is called the domination number of GP(n,k). In this paper we give a dynamic programming algorithm for computing the domination number of a given GP(n,k) in O(n) time and space for every k=O(1).