The correct statements are C and F.
There are two elementary types of pigments, which are responsible for the color of the coat, that is, phaeomelanin and eumelanin. Eumelanin is basically a black pigment and cells produced by it are responsible for a black dog coat color. However, there are genes that result in changes in eumelanin to produce brown, gray, or dusty pale brown coat color. The genes responsible for this change leads to the modifications in the creation of the eumelanin in the cells.
Due to this reason, dusty pale brown and gray dogs are considered as dilutes. Eumelanin can also be witnessed in eyes and nose. On the basis of the genes in dogs, the nose can be brown, black, dusty pale brown, or gray. The other pigments, that is, phaeomelanin is red. Most of the dogs exhibit both phaeomelanin and eumelanin, and the manner in which these two pigments get amalgamated is controlled by agouti locus.
The white color in dogs is not stimulated by any pigment, but by the cells that do not possess the capability to produce any kind of pigment. The entire animal can be affected in a different manner to albinos, or it can be restricted like the white coat patterns.
The correct statements regarding the mode of inheritance of the coat color genes are:
1) One of the genes modifies the expression of the other.
2) One of the genes is autosomal, and the other is X-linked.