2 problems

Odd-dimensional nonexistence conjecture. For any odd dimension, there is no weakly Hadamard diagonalizable graph whose Laplacian eigenspaces have equal algebraic and geometric mult…

Let $T$ be a tree, let $P_2$ and $P_3$ denote the paths on two and three vertices, and say that $T$ has adjacency perfect state transfer if its adjacency-matrix continuous-time qua…