ON THE DOMINATION AND TOTAL DOMINATION NUMBERS OF CAYLEY SUM GRAPHS OVER Z(n)

Let G be a finite Abelian group and S be a subset of G. The Cayley sum graph Cay(+)(G, S) of G with respect to S is a graph whose vertex set is G and two vertices 9 and h are joined by an edge if and only if g + h is an element of S. In this paper, we prove some basic facts on the domination and total domination numbers of Cayley sum graphs. Then, we find the sharp bounds for domination number of Cay(+) (Z(n), S), where S = {1, 2,..., k} and n, k are positive integers with 1 <= k <= (n 1)/2.