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.