  We study the formation of stationary localized states using the discrete
nonlinear Schr\"{o}dinger equation in a Cayley tree with connectivity $K$. Two
cases, namely, a dimeric power law nonlinear impurity and a fully nonlinear
system are considered. We introduce a transformation which reduces the Cayley
tree into an one dimensional chain with a bond defect. The hopping matrix
element between the impurity sites is reduced by $1/\surd K$. The transformed
system is also shown to yield tight binding Green's function of the Cayley
tree. The dimeric ansatz is used to find the reduced Hamiltonian of the system.
Stationary localized states are found from the fixed point equations of the
Hamiltonian of the reduced dynamical system. We discuss the existence of
different kinds of localized states. We have also analyzed the formation of
localized states in one dimensional system with a bond defect and nonlinearity
which does not correspond to a Cayley tree. Stability of the states is
discussed and stability diagram is presented for few cases. In all cases the
total phase diagram for localized states have been presented.
