  In the counting Graph Homomorphism problem (#GraphHom) the question is: Given
graphs G,H, find the number of homomorphisms from G to H. This problem is
generally #P-complete, moreover, Cygan et al. proved that unless the ETH is
false there is no algorithm that solves this problem in time
O(|V(H)|^{o(|V(G)|)}. This, however, does not rule out the possibility that
faster algorithms exist for restricted problems of this kind. Wahlstrom proved
that #GraphHom can be solved in plain exponential time, that is, in time
k^{|V(G)|+V(H)|}\poly(|V(H)|,|V(G)|) provided H has clique width k. We
generalize this result to a larger class of graphs, and also identify several
other graph classes that admit a plain exponential algorithm for #GraphHom.
