Tight Frame Graphs Arising as Line Graphs

  • Veronika Furst Fort Lewis College
  • Howard Grotts Fort Lewis College
Keywords: tight frame graph; dual multiplicity graph; line graph; Gram matrix; Laplacian matrix

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.

Author Biography

Howard Grotts, Fort Lewis College

Graduate student in the Department of Mathematical Sciences, University of Montana, beginning Fall 2020.

Published
2021-01-20
How to Cite
Furst, V., & Grotts, H. (2021). Tight Frame Graphs Arising as Line Graphs. The PUMP Journal of Undergraduate Research, 4, 1-19. Retrieved from https://journals.calstate.edu/pump/article/view/2415