On some topological indices over rectangular grids

A topological index is a real number related to a graph, which is considered as a structural invariant. Some examples are Sombor index, Randic index, Zagreb indices, and Harmonic index. In the present paper, we consider the function Ind from the set of all rectangular grids to the set of real numbers, which assigns to each rectangular grid, one of its above indices. Then we show that the only non-degenerate indices over retangular grids, are Sombor index and Randic index, while Zagreb indices and the Harmonic index are degenerate. In the following, we determine rectangular grids with  xed diameter d, where maximum and minimum of the above indices occures on them, in the case m  3; n  3. Finally, we  nd the amounts of these indices.