Average mixing matrix of trees [article]

Chris Godsil, Krystal Guo, John Sinkovic
2017 arXiv   pre-print
We investigate the rank of the average mixing matrix of trees, with all eigenvalues distinct. The rank of the average mixing matrix of a tree on n vertices with n distinct eigenvalues is upper-bounded by n/2. Computations on trees up to 20 vertices suggest that the rank attains this upper bound most of the times. We give an infinite family of trees whose average mixing matrices have ranks which are bounded away from this upper bound. We also give a lower bound on the rank of the average mixing matrix of a tree.
arXiv:1709.07907v1 fatcat:7oaxql7tzfcghghctsxrz3bgoy