Tight Frame Graphs Arising as Line Graphs

TL;DR

This paper classifies specific line graphs that can be represented as tight frames, linking graph theory with frame theory and improving previous embedding results.

Contribution

It provides a classification of certain line graphs as tight frame graphs and enhances understanding of their embedding properties.

Findings

Identified classes of line graphs that are tight frame graphs

Improved previous results on embedding frame graphs in tight frame graphs

Connected graph spectral properties with frame representations

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.