Two vertices $ a $ and $ b $ in a graph $ X $ are cospectral if the vertex-deleted subgraphs
$ X\setminus a $ and $ X\setminus b $ have the same characteristic polynomial. In this …

Quantum walks on graphs are fundamental to quantum computing and have led to many
interesting open problems in algebraic graph theory. This review article highlights three key …

The adjacency matrix of a graph is the Hamiltonian for a continuous-time quantum walk on
the vertices of. Although the entries of the adjacency matrix are integers, its eigenvalues are …

Two vertices a and b in a graph X are cospectral if the vertex-deleted subgraphs X\a and X\b
have the same characteristic polynomial. In this paper we investigate a strengthening of this …

The (standard) average mixing matrix of a continuous-time quantum walk is computed by
taking the expected value of the mixing matrices of the walk under the uniform sampling …

The continuous-time quantum walk is a particle evolving by Schrödinger's equation in
discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is …

We study the diagonal entries of the average mixing matrix of continuous quantum walks.
The average mixing matrix is a graph invariant; it is the sum of the Schur squares of spectral …

We study the average probability that a discrete-time quantum walk finds a marked vertex on
a graph. We first show that, for a regular graph, the spectrum of the transition matrix is …

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 …

We study the diagonal entries of the average mixing matrix of continuous quantum walks.
The average mixing matrix is a graph invariant; it is the sum of the Schur squares of spectral …