A subset D of vertices of a graph G is a dominating set if for each u > V(G)\D, u is adjacent to some vertex v > D. The domination number, (G) of G, is the minimum cardinality of a dominating set of G. For an even integer n >= 2 and 1 B B log2 n, a Knödel graph W,n is a -regular bipartite graph of even order n, with vertices (i, j), for i = 1, 2 and 0 B j B n~2 − 1, where for every j, 0 B j B n~2 − 1, there is an edge between vertex (1, j) and every vertex (2, (j + 2k − 1) mod (n/2)), for k = 0, 1,, − 1. In this paper, we determine the domination number in 4-regular Knödel graphs W4,n.
