Codeterminantal graphs

Aida Abiad, Carlos Alfaro, Kristin Heysse, Marcos Vargas

Research output: Contribution to journalArticlepeer-review


We introduce the concept of codeterminantal graphs, which generalize the concepts of cospectral and coinvariant graphs. To do this, we investigate the relationship of the spectrum and the Smith normal form (SNF) with the determinantal ideals. We establish a necessary and sufficient condition for graphs to be codeterminantal on R[x], and we present some computational results on codeterminantal graphs up to 9 vertices. Finally, we show that complete graphs and star graphs are determined by the SNF of its distance Laplacian matrix.

Original languageEnglish
Pages (from-to)1-25
Number of pages25
JournalLinear Algebra and its Applications
Publication statusPublished - 1 Oct 2022


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