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A chemical graph or a molecular graph is a simple graph related to the structure of a chemical compound. The connectivity indices are applied to measure the chemical characteristics of compounds in Chemical Graph Theory. In this paper, we determine the multiplicative atom bond connectivity index and geometric arithmetic index of three families of dendrimer nanostars.Keywords: multiplicative atom bond connectivity index, multiplicative geometricarithmetic index, dendrimer nanostar.

The study of the topological indices in the quantitative structure–activity and structure–property models are used to predict the physicochemical properties of the chemical compounds. In this paper, we analyze the molecular structure of hyaluronic acid conjugated with methotrexate which is used in anticancer drugs. We obtain the exact formulas for several new Sombor‐type vertex‐degree‐based topological indices and the Banhatti–Sombor‐type vertex‐degree‐based topological indices of the molecular structure of hyaluronic acid–methotrexate conjugate using the graph theory and the edge‐partition approach. We use Matlab and Mathematica software to evaluate the results and accuracy of calculations. The numerical results in this study can help understand the biological activity of the chemical structure of these drugs.

A set D of vertices in a graph G = (V, E) is a total dominating set if every vertex of G is adjacent to some vertex in D. A total dominating set D of G is said to be weak if every vertexThe weak total domination number γ wt (G) of G is the minimum cardinality of a weak total dominating set of G. A total dominating set D of G is said to be strong if every vertexThe strong total domination number γ st (G) of G is the minimum cardinality of a strong total dominating set of G. We present some bounds on weak and strong total domination number of a graph.

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