7 problems

Coutinho–Liu's conjecture. No tree with at least four vertices admits perfect state transfer in the adjacency matrix model.

Let $X$ be a simple connected unweighted graph on an odd number of vertices. Odd-order Laplacian PST conjecture. Laplacian perfect state transfer does not occur in $X$. This extend…

Let $n,m \geq 3$ with $(n,m) \neq (4,4)$. A toroidal $(n,m)$-grid is the toroidal grid with parameters $n$ and $m$, and periodic means periodic under the discrete-time quantum walk…

Let $Z$ be the graph shown in Figure 6: a longer path $X$ joins the relevant subgraphs, with vertices $a,b,c,d$ labelled as in that figure. No-perfect-state-transfer conjecture. Pe…

No state transfer in trees conjecture. No tree on four or more vertices admits perfect state transfer.

A complex unit gain graph is a graph whose adjacency matrix has complex entries, with each nonzero entry of unit magnitude. A graph has property $\mathbb{T}$ if all nonzero coeffic…

Let $P_n$ be a path graph of arbitrary length, with a potential placed on its two endpoints and corresponding Hamiltonian $H=A+Q$, where $A$ is the adjacency matrix and $Q$ is the…