On some topological invariants of Parikh word representable graphs

The study of Parikh word representable graphs $G(w)$ related to words $w$ that are finite sequence of symbols has been developed in the recent years. On the other hand, several topolgical indices have been defined in terms of graph parameters and studied for different class of graphs. In this paper, we obtain formulas for first and second Zagreb index of Parikh word representable graphs with binary core word $aub$ over alphabets $a,b$. Also, we obtain formulas for the reduced first and second Zagreb indices, forgotten topological index, reduced forgotten topological index, and hyper-Zagreb index.