Abstract
Let \(G=(V,E)\) be a simple undirected and connected graph on \(n\) vertices. The Graovac-Ghorbani (\(ABC_{GG}\)) index of a graph \(G\) is defined as
\[
ABC_{GG}(G)= \sum_{uv \in E} \sqrt{\frac{n(u)+n(v)-2} {n(u) n(v)}}\,,
\]
where \(n(u)\) is the number of vertices closer to vertex \(u\) than vertex \(v\) and \(n(v)\) is defined analogously. This paper is a survey of topological Graovac-Ghorbani index of a graph \(G\). It contains results on \(ABC_{GG}\) which are known until this moment and some conjectures.
