On the construction of equiangular frames from graphs

Shayne Waldron


We give details of the 1--1 correspondence between equiangular frames of n vectors for R^d and graphs with n vertices. This has been studied recently for tight equiangular frames because of applications to signal processing and quantum information theory. The nontight examples given here (which correspond to graphs with more than 2 eigenvalues) have the potential for similar applications, e.g., the frame corresponding to the 5-cycle graph is the unique Grassmannian frame of 5 vectors in R^3. Further, the associated canonical tight frames have a small number of angles in many cases.

Keywords: finite frame, tight frame, Grassmannian frame, mutually unbiased basis, two angle frame, Seidel matrix, adjacency matrix, algebraic graph theory, signal processing, information theory,

Math Review Classification: Primary 42C15, 05C50; Secondary 05C90, 52B15

Length: 17 pages

Last Updated: 22 January 2009