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

• Aida Abiad ; Boris Brimkov ^[1] ; Sakander Hayat ^[4] ; Antonina P. Khramova ^[2] ; Jack H. Koolen ^[3]
  1. [1] Slippery Rock University

     Slippery Rock University

     Borough of Slippery Rock, Estados Unidos

     
  2. [2] Eindhoven University of Technology

     Eindhoven University of Technology

     Países Bajos

     
  3. [3] University of Science and Technology of China

     University of Science and Technology of China

     China

     
  4. [4] GIK Institute of Engineering Sciences and Technology, Topi, Swabi, Pakistan

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• Localización: Discrete Mathematics Days 2022 / Luis Felipe Tabera Alonso (ed. lit.), 2022, ISBN 978-84-19024-02-2, págs. 11-16
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.