Journal of Integer Sequences, Vol. 15 (2012), Article 12.5.1

On the Modes of the Independence Polynomial of the Centipede

Moussa Benoumhani
Department of Mathematics
Faculty of Sciences
Al-Imam University
P. O. Box 90950
Riyadh 11623
Saudi Arabia


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.

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(Concerned with sequences A000032 A000045 A028859 A129722.)

Received October 21 2011; revised version received April 14 2012. Published in Journal of Integer Sequences, April 20 2012.

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