Domination in 4-regular Knodel graphs

A subset D of vertices of a graph G is a dominating set if for each u is an element of V(G)\ D, u is adjacent to some vertex v is an element of D. The domination number, gamma(G) of G, is the minimum cardinality of a dominating set of G. For an even integer n >= 2 and 1 <= Delta <= [log(2) n], a Knodel graph W-Delta,W-n is a Delta-regular bipartite graph of even order n, with vertices (i, j), for i = 1, 2 and 0 <= j <= n/2 - 1, where for every j, 0 <= j <= n/2 - 1, there is an edge between vertex (1, j) and every vertex (2, (j + 2(k) - 1) mod (n/2)), for k = 0, 1, . . . , Delta - 1. In this paper, we determine the domination number in 4-regular Knodel graphs W-4,W-n.