  A $(k,g)$-cage is a $k$-regular simple graph of girth $g$ with minimum
possible number of vertices. In this paper, $(k,g)$-cages which are Moore
graphs are referred as minimal $(k,g)$-cages. A simple connected graph is
called distance regular(DR) if all its vertices have the same intersection
array. A bipartite graph is called distance biregular(DBR) if all the vertices
of the same partite set admit the same intersection array. It is known that
minimal $(k,g)$-cages are DR graphs and their subdivisions are DBR graphs. In
this paper, for minimal $(k,g)$-cages we give a formula for distance spectral
radius in terms of $k$ and $g$, and also determine polynomials of degree
$[\frac{g}{2}]$, which is the diameter of the graph. This polynomial gives all
distance eigenvalues when the variable is substituted by adjacency eigenvalues.
We show that a minimal $(k,g)$-cage of diameter $d$ has $d+1$ distinct distance
eigenvalues, and this partially answers a problem posed in [5]. We prove that
every DBR graph is a $2$-partitioned transmission regular graph and then give a
formula for its distance spectral radius. By this formula we obtain the
distance spectral radius of subdivision of minimal $(k,g)$-cages. Finally we
determine the full distance spectrum of subdivision of some minimal
$(k,g)$-cages.
