Domination in Cayley graphs: A survey

Let Omega be a symmetric generating set of a finite group Gamma. Assume that (Gamma, Omega) be such that Gamma = (Omega) and Omega satisfies the two conditions C-1: the identity element e epsilon Omega and C-2: if a epsilon Omega, then a(-1) epsilon Omega. Given (Gamma, Omega) satisfying C-1 and C-2, define a Cayley graph G = Cay(Gamma, Omega) with V(G) = Gamma and E(G) = {(x, y)a vertical bar x, y epsilon Gamma, a epsilon Omega and y = xa}. When Gamma = Z(n)= (Omega), it is called as circulant graph and denoted by Cir(n, Omega). In this paper, we give a survey about the results on dominating sets in Cayley graphs and circulant graphs. (C) 2017 Kalasalingam University. Production and Hosting by Elsevier B.Y.