2 citations · 4 across the 5 of their papers we have counts for
6 papers · 1 filter
A note on Global Positioning System (GPS) and Euclidean distance matrices
A. Y. Alfakih
Let be an Euclidean distance matrix (EDM) with embedding dimension ; and let be a given vector. In this note, we consider the problem of finding a v…
On the Colin de Verdiere graph number and penny graphs
A. Y. Alfakih
The Colin de Verdiere number of graph G, denoted by μ(G), is a spectral invariant of G that is related to some of its topological properties. For example, μ(G) \leq 3 iff G is plan…
On Theorems of Sinajova, Rankin and Kuperberg Concerning Spherical Point Configurations
A. Y. Alfakih
This note presents simple linear algebraic proofs of theorems due to Sinajova, Rankin and Kuperberg concerning spherical point configurations. The common ingredient in these proofs…
On Unit Spherical Euclidean Distance Matrices Which Differ in One Entry
A. Y. Alfakih
A unit spherical Euclidean distance matrix (EDM) D is a matrix whose entries can be realized as the interpoint (squared) Euclidean distances of n points on a unit sphere. In this p…
On Representations of Graphs as Two-Distance Sets
A. Y. Alfakih
Let a \neq b be two positive scalars. A Euclidean representation of a simple graph G in R^r is a mapping of the nodes of G into points in R^r such that the squared Euclidean distan…
Universal Rigidity of Bar Frameworks via the Geometry of Spectrahedra
A. Y. Alfakih
A bar framework (G,p) in dimension r is a graph G whose vertices are points p^1,...,p^n in R^r and whose edges are line segments between pairs of these points. Two frameworks (G,p)…