Resumen de Extending a conjecture of Graham and Lovász on the distance characteristic polynomial

Aida Abiad, Boris Brimkov, Sakander Hayat, Antonina P. Khramova, Jack H. Koolen

• Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients ofthe distance characteristic polynomial of a tree of order n is unimodal with the maximumvalue occurring at ⌊n2⌋. In this paper we extend this old conjecture to block graphs. Inparticular, we prove the unimodality part and we establish the peak for several extremalcases of block graphs with small diameter.