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Sierpiński graphs are extensively studied graphs of fractal nature with applications in topology, mathematics of Tower of Hanoi and computer science. The generalized Sierpiński graphs are defined by replication of exactly the same graph, yielding self-similar graph. Certain graph invariants referred to as topological indices are used to determine a large number of properties like physico-chemical properties, thermodynamic properties, chemical activity and biological activity of chemical graphs. In QSAR/QSPR study, these graph invariants play a vital role.In this article, we study the topological indices of generalized Sierpiński and extended Sierpiński graphs with an arbitrary base graph. We obtain bounds for the atom-bond connectivity index, harmonic index, Zagreb indices and sum-connectivity index for the generalized Sierpiński graphs and extended Sierpiński graphs. [ABSTRACT FROM AUTHOR]

In this paper, we establish bounds on the domination number and the metric dimension of the co-normal product graph GH of two simple graphs G and H in terms of parameters associated with G and H. We also give conditions on the graphs G and H for which the domination number of GH is 1, 2, and the domination number of G. Moreover, we give formulas for the metric dimension of the co-normal product GH of some families of graphs G and H as a function of associated parameters of G and H. [ABSTRACT FROM AUTHOR]