  Graham and Lov\'{a}sz conjectured in 1978 that the sequence of normalized
coefficients of the distance characteristic polynomial of a tree of order $n$
is unimodal with the maximum value occurring at $\lfloor\frac{n}{2}\rfloor$. In
this paper we investigate this problem for block graphs. In particular, we
prove the unimodality part and we establish the peak for several extremal cases
of uniform block graphs with small diameter.
