On the GraovacGhorbani and AtomBond Connectivity Indices of Graphs from Primary Subgraphs

Let be a finite simple graph. The Graovac-Ghorbani index of a graph is defined as ∑ √ where is the number of vertices closer to vertex than vertex of the edge . is defined analogously. The atom-bond connectivity index of a graph G is defined as ∑ √ where is the degree of vertex in . Let be a connected graph constructed from pairwise disjoint connected graphs by selecting a vertex of , a vertex of , and identifying these two vertices. Then continue in this manner inductively. We say that is obtained by point-attaching from and that 's are the primary subgraphs of . In this paper, we give some upper bounds on Graovac-Ghorbani and atom-bond connectivity indices for these graphs. Additionally, we consider some particular cases of these graphs that are of importance in chemistry and study their Graovac- Ghorbani and atom-bond connectivity indices.