DMS Combinatorics Seminar

Speaker: Steve Butler (Iowa State University)

Title: Forming cospectral graphs by coalescing 

Abstract: Spectral graph theory looks at the interplay between graphs and the eigenvalues of particular matrices associated with graphs. One way to understand the shortcomings of particular matrices is through the study of "cospectral graphs" (nonisomorphic graphs with the same eigenvalues). A well-known method of forming cospectral graphs is through coalescing, the act of gluing graphs by identifying vertices together. We give necessary and sufficient conditions for forming cospectral graphs by coalescing for matrices in the same family as the adjacency or Laplacian using cycle decomposition arguments. We also will give a sufficient condition for forming cospectral graphs by coalescing for the distance matrix using block similarity arguments.

This is based on work done in the 2022 and 2023 REUs at Iowa State University.