Domination Number of Cayley Graphs on Finite Abelian Groups

In this paper, we study the domination parameters of Cayley graphs constructed out of Z(p) x Z(m), where m is an element of {p(alpha), p(alpha)q(beta), p(alpha)q(beta)r(gamma)} and p, q, r are prime numbers. Indeed, we give a lower bound for domination number of Gamma = Cay(Z(2) x Z(2 alpha p1)(alpha 1)p(2)(alpha 2)...p(k)(alpha k), Phi), where Phi = phi(2) x phi 2(2 alpha p1)(alpha 1)p(2)(alpha 2)...p(k)(alpha k), p(1) = 3 and for 1 <= i <= k - 1; p(i+1) is the first prime greater than p(i); alpha >= 2 and alpha(1); alpha(2)... alpha(k) are positive integers, and um phi(m) = {l vertical bar 1 <= l < m, gcd(l,m) = 1}.