If X is a graph with adjacency matrix A, then we define H (t) to be the operator exp (itA). We
say that we have perfect state transfer in X from the vertex u to the vertex v at time τ if the uv …

In this paper, we shall give a survey of applications of the theory of graph spectra to
Computer Science. Eigenvalues and eigenvectors of several graph matrices appear in …

We provide a brief survey of perfect state transfer in quantum walks on finite graphs. The
ability to transfer a quantum state from one part of a quantum computer to another is a key …

arXiv:1809.09829v3 [math.CO] 22 Apr 2022 Eigenvalues of Cayley graphs Page 1 arXiv:1809.09829v3
[math.CO] 22 Apr 2022 Eigenvalues of Cayley graphs Xiaogang Liu∗ School of Mathematics …

A graph G of order n is called hyperenergetic if E (G)> 2n-2, where E (G) denotes the energy
of G. The unitary Cayley graph Xn has vertex set Zn={0, 1, 2,…, n-1} and vertices a and b are …

The distance energy of a graph G is a recently developed energy-type invariant, defined as
the sum of absolute values of the eigenvalues of the distance matrix of G. There was a vast …

We propose new families of graphs which exhibit quantum perfect state transfer. Our
constructions are based on the join operator on graphs, its circulant generalizations, and the …

In this paper we answer the question of when circulant quantum spin networks with nearest-
neighbor couplings can give perfect state transfer. The network is described by a circulant …

Recently, there are extensive studies on perfect state transfer on graphs due to their
significant applications in quantum information processing and quantum computations …

This work is based on ideas of Ilić [A. Ilić, The energy of unitary Cayley graphs, Linear
Algebra Appl. 431 (2009) 1881–1889] on the energy of unitary Cayley graph. For a finite …