Abstract
The Graovac-Ghorbani (\(ABC_{GG}\)) index of a graph is a distance-based topological descriptor which is an analog of the atom-bond connectivity (ABC) Index. In [9], Furtula showed that, tested on alkans, \(ABC_{GG}\) gives better prediction in the case of entropy and acentric factor than \(ABC\) index. In [5] Dimitrov et al. conjectured that among all trees on \(n\) vertices with the maximum degree $\Delta$ almost dendrimers are trees which maximize \(ABC_{GG}\) index. In this paper we present a mathematical proof of the established conjecture by showing that almost dendrimers are extremal trees among all trees with \(n\) vertices and maximum degree at most \(\Delta\).
