On some topological indices for the orbit graph of dihedral groups (Q6558938)

A topological index (TI) is a numerical parameter associated to a graph which is invariant under graph isomorphism. They are of great importance in chemical graph theory. On the other hand, given a group \(G\), let \(\Gamma_{G}\) be the orbit graph of \(G\), with non-central orbits in the subset of order two commuting elements in \(G\), and the vertices of \(\Gamma_{G}\) are connected if they are conjugate.\N\NThe authors of this paper compute the Wiener index, the first, the second and the third Zagreb index, the hyper first and the hyper second Zagreb index, the modified first Zagreb ind, the Schultz and the modified Schultz index, the forgotten index, the Somber index, the Randic and the reciprocal Randic index for the orbit graph of the dihedral group \(D_{t}\). Moreover, they obtain relationships between these indices with the Wiener index and the polynomials of indices for the orbit graphs of \(D_{t}\).