Tight Frame Graphs Arising as Line Graphs

Abstract

Dual multiplicity graphs are those simple, undirected graphs that have a weighted Hermitian adjacency matrix with only two distinct eigenvalues. From the point of view of frame theory, their characterization can be restated as which graphs have a representation by a tight frame. In this paper, we classify certain line graphs that are tight frame graphs and improve a previous result on the embedding of frame graphs in tight frame graphs.

14 pages, 6 figures. Version 2 of this paper adds a reference, adds a figure, and includes minor corrections and revisions