on the graovc-ghorbani and atom-bond connectivity indices of graphs from primary subgraphs

Let g=(v,e) be a finite simple graph. the graovac-ghorbani index of a graph g is defined as abcgg(g)=∑uv∈e(g) √((nu(uv,g)+nv(uv,g)-2)/(nu(uv,g)nv(uv,g))), where nu(uv,g) is the number of vertices closer to vertex u than vertex v of the edge uv∈e(g).  nv(uv,g) is defined analogously. the atombond connectivity index of a graph g is defined as abc(g)=∑uv∈e(g)√((du+dv-2)(dudv)), where du is the degree of vertex u in g. let g be a connected graph constructed from pairwise disjoint connected graphs g1,...,gk by selecting a vertex of g1, a vertex of g2, and identifying these two vertices. then continue in this manner inductively. we say that g is obtained by point-attaching from g1,...,gk and that gi ’s are the primary subgraphs of g. in this paper, we give some lower and upper bounds on graovac-ghorbani and atombond 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.