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1. Suppose we have perfect state transfer from $a$ to $b$ at some time $t$ in the continuous quantum walk of $X$. Does it follow that the sum of the eigenvalues in the eigenvalue support of $a$ is equal to zero?
2. Is there a tree with more that four vertices that admits perfect state transfer?
3. Find a combinatorial characterization of strongly cospectral vertices.
4. Does the cycle on nine vertices admit uniform mixing? Is there an odd cycle with morre that three vertices that admits uniform mixing?
5. Is there a characterization of the connection sets of the cubelike graphs that admit perfect state transfer that is polynomial time in the size of the connection set?