Abstract
A topological index is a quantity that is somehow calculated from a graph (molecular structure), which reflects relevant structural features of the underlying molecule. It is, in fact, a numerical value associated with the chemical constitution for the correlation of chemical structures with various physical properties, chemical reactivity, or biological activity. A large number of properties like physicochemical properties, thermodynamic properties, chemical activity, and biological activity can be determined with the help of various topological indices such as atom-bond connectivity indices, Randić index, and geometric arithmetic indices. In this paper, we investigate topological properties of two graphs (commuting and noncommuting) associated with an algebraic structure by determining their Randić index, geometric arithmetic indices, atomic bond connectivity indices, harmonic index, Wiener index, reciprocal complementary Wiener index, Schultz molecular topological index, and Harary index.
Highlights
In quantitative structure-activity relationship (QSAR)/ quantitative structure-property relationship (QSPR) study, physicochemical properties and topological indices such as Randicindex, atom-bond connectivity (ABC) index, and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds
A topological index is designed by transforming a chemical structure into a numerical number
An algebraic structure plays a vital role in chemistry to form chemical compound structures and in investigating various chemical properties of chemical compounds in these structures
Summary
In quantitative structure-activity relationship (QSAR)/ quantitative structure-property relationship (QSPR) study, physicochemical properties and topological indices such as Randicindex, atom-bond connectivity (ABC) index, and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. A topological index is designed by transforming a chemical structure into a numerical number It correlates certain physicochemical properties such as boiling point, stability, and strain energy of chemical compounds of a molecular structure (graph). (i) e commuting graph of a nonabelian group Γ is denoted by ΓG C(Γ, Ω) with vertex set Ω ⊆ Γ. E concept of commuting graphs on noncentral elements of a group has been studied by various researchers (see [16, 17]). (ii) e noncommuting graph of a nonabelian group GΓ is a graph with vertex set V(G1) ∪ V(G2), and two distinct vertices u and v in GΓ form an edge if uv ≠ vu in Γ. Is paper aimed at investigating all the topological properties (listed in Table 1) of commuting and noncommuting graphs associated with the group of symmetries.
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