Some remarks on Balaban and sum-Balaban index

  • Martin Knor Slovak University of Technology in Bratislava, Slovakia
  • Jozef Komorník Comenius University, Slovakia
  • Riste Škrekovski University of Ljubljana, Slovenia, and Faculty of Information Studies, Slovenia, and University of Primorska, Slovenia
  • Aleksandra Tepeh Faculty of Information Studies, Slovenia, and University of Maribor, Slovenia
Keywords: Topological index, Balaban index, sum-Balaban index, Randi´c index


In the paper we study maximal values of Balaban and sum-Balaban index, and correct some results appearing in the literature which are only partially correct. Henceforth, we were able to solve a conjecture of M. Aouchiche, G. Caporossi and P. Hansen regarding the comparison of Balaban and Randić index. In addition, we showed that for every k and large enough n, the first k graphs of order n with the largest value of Balaban index are trees. We conclude the paper with a result about the accumulation points of sum-Balaban index.