  For random matrices with tree-like structure there exists a recursive
relation for the local Green functions whose solution permits to find directly
many important quantities in the limit of infinite matrix dimensions. The
purpose of this note is to investigate and compare expressions for the spectral
density of random regular graphs, based on easy approximations for real
solutions of the recursive relation valid for trees with large coordination
number. The obtained formulas are in a good agreement with the results of
numerical calculations even for small coordination number.
