On the Modes of the Independence Polynomial of the Centipede
Department of Mathematics
Faculty of Sciences
P. O. Box 90950
The independence polynomial of the graph called the
centipede has only real
zeros. It follows that this polynomial is log-concave, and hence unimodal.
Levit and Mandrescu gave a conjecture about the mode of this polynomial. In
this paper, the exact value of the mode is determined, and some central
limit theorems for the sequence of the coefficients are established.
Full version: pdf,
(Concerned with sequences
Received October 21 2011;
revised version received April 14 2012.
Published in Journal of Integer Sequences, April 20 2012.
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