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

Extending a conjecture of Graham and Lov\'{a}sz on the distance characteristic polynomial