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Let $G=(V,E)$ be a finite simple graph. The Graovac-Ghorbani index of a graphG is defined as $ABC_{GG}(G)=\sum_{uv\inE(G)}\sqrt{\frac{n_u(uv,G)+n_v(uv,G)-2}{n_u(uv,G)n_v(uv,G)}},$ where$n_u(uv,G)$ is the number of vertices closer to vertex $u$ than vertex $v$ ofthe edge $uv\in E(G)$. $n_v(uv,G)$ is defined analogously. The atom-bondconnectivity index of a graph G is defined as $ABC(G)=\sum_{uv\inE(G)}\sqrt{\frac{d_u+d_v-2}{d_ud_v}},$ where $d_u$ is the degree of vertex $u$in $G$. Let $G$ be a connected graph constructed from pairwise disjointconnected graphs $G_1,\ldots ,G_k$ by selecting a vertex of $G_1$, a vertex of$G_2$, and identifying these two vertices. Then continue in this mannerinductively. We say that $G$ is obtained by point-attaching from $G_1, \ldots,G_k$ and that $G_i$'s are the primary subgraphs of $G$. In this paper, we givesome lower and upper bounds on Graovac-Ghorbani and atom-bond connectivityindices for these graphs. Additionally, we consider some particular cases ofthese graphs that are of importance in chemistry and study theirGraovac-Ghorbani and atom-bond connectivity indices.

On the Graovac-Ghorbani and atom-bond connectivity indices of graphs from primary subgraphs