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

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

doi:10.1016/j.laa.2023.03.027

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

Aida Abiad, Jack H Koolen + Show 3 more

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https://doi.org/10.1016/j.laa.2023.03.027

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Journal: Linear Algebra and Its Applications	Publication Date: Apr 12, 2023
Citations: 1	License type: cc-by

Affiliation: Vrije Universiteit Brussel, Ghent University, Eindhoven University of Technology, University of Science and Technology of China, Universiti Brunei Darussalam, Slippery Rock University

#Block Graphs #Coefficients Of Characteristic Polynomial + Show 5 more

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Abstract

Graham and Lovász 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 ⌊n2⌋. 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.

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