The integer {k}-domination number of circulant graphs

Let G = (V, E) be a simple undirected graph. G is a circulant graph defined on V = Z(n) with difference set D subset of {1,2, ..., left perpendicularn/2right perpendicular} provided two vertices i and j in Z(n) are adjacent if and only if min{vertical bar i - j vertical bar, n - vertical bar i - vertical bar} is an element of D. For convenience, we use G(n; D) to denote such a circulant graph. A function f: V(G) -> N boolean OR {0} is an integer {k}-domination function if for each v is an element of V (G), Sigma(u is an element of NG[v] )f(u) >= k.. By considering all {k}-domination functions f, the minimum value of Sigma(v is an element of V(G)) f(v) is the {k}-domination number of G, denoted by gamma k(G). In this paper, we prove that if D = {1, 2, ..., t}, 1 <= t <= n-1/2, then the integer {k}-domination number of G(n; D) is inverted right perpendicularkn/2t+1inverted left perpendicular.