Let G1 and G2 be disjoint copies of a graph G, and let f:V(G1)→V(G2) be a function. Then a \emph{functigraph} C(G,f)=(V,E)
has the vertex set V=V(G1)∪V(G2) and the edge set E=E(G1)∪E(G2)∪{uv∣u∈V(G1),v∈V(G2),v=f(u)}. A functigraph is a
generalization of a \emph{permutation graph} (also known as a \emph{generalized
prism}) in the sense of Chartrand and Harary. In this paper, we study
domination in functigraphs. Let γ(G) denote the domination number of
G. It is readily seen that γ(G)≤γ(C(G,f))≤2γ(G). We
investigate for graphs generally, and for cycles in great detail, the functions
which achieve the upper and lower bounds, as well as the realization of the
intermediate values.Comment: 18 pages, 8 figure