To solve the inverse gravimetric problem, i.e. to reconstruct the Earth's mass density distribution by using the gravitational potential, we introduce a spline interpolation method for the ellipsoidal Earth model, where the ellipsoid has a rotational symmetry. This problem is ill-posed in the sense of Hadamard as the solution may not exist, it is not unique and it is not stable. Since the anharmonic part (orthogonal complement) of the density function produces a zero potential, we restrict our attention only to reconstruct the harmonic part of the density function by using the gravitational potential. This spline interpolation method gives the existence and uniqueness of the unknown solution. Moreover, this method represents a regularization, i.e. every spline continuously depends on the given gravitational potential. These splines are also combined with a multiresolution concept, i.e. we get closer and closer to the unknown solution by increasing the scale and adding more and more data at each step.

If the degrees of any two consecutive vertices differ by exactly one, the graph is called a stepwise irregular graph. The study of choosing specific vertices in an ordered subset of the vertex set such that no two vertices have the same representations with regard to the chosen subset is known as resolving parameters. This concept has been expanded for edges as well as a combined version of both. We examine a unique unicyclic stepwise irregular graph and an extended structure of stepwise irregular graph in terms of resolvability parameters to connect the stepwise irregular graph and resolving parameter concepts.