In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

A set S of unit vectors in n−dimensional Euclidean space is called spherical two-distance set, if there are two numbers a and b so that the inner products of distinct vectors of S are either a or b. The largest cardinality g(n) of spherical two-distance sets does not exceed n(n+3)/2. This upper bound is known to be tight for n = 2, 6, 22. The set of midpoints of the edges of a regular simplex g...

We characterize the denseness of singular set distance function from a $\mathcal{C}^1$-hypersurface in terms an inner ball condition and we address problem existence viscosity solutions Eikonal equation whose (i.e. non-differentiability points) is not no-where dense.

We address the problem of reconstructing a set points on line or loop from their unassigned noisy pairwise distances. When lie line, is known as turnpike; when they are loop, it beltway. approximate by discretizing domain and representing $N$</inline-fo...