Some remarks on Balaban and sum-Balaban index. (English) Zbl 1441.05054
Summary: 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.
MSC:
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
| 05C12 | Distance in graphs |
| 05C90 | Applications of graph theory |
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