On Some Topological Indices for the Orbit Graph of Dihedral Groups

Abstract

Let ΓG be the orbit graph of G, with non-central orbits in the subset of order two commuting elements in G, and the vertices of ΓG connected if they are conjugate. The main objective of this study is to compute several topological indices for the orbit graph of a dihedral group, including the Wiener index, the Zagreb index, the Schultz index, and others. We also develop a relationship between the Wiener index and the other indices for the dihedral group’s orbit graph. Furthermore, their polynomial has been computed as well.