# Some classes of integral circulant graphs either allowing or not allowing perfect state transfer

@article{Tasic2009SomeCO, title={Some classes of integral circulant graphs either allowing or not allowing perfect state transfer}, author={Milan B. Tasic and Marko D. Petkovi{\'c}}, journal={Appl. Math. Lett.}, year={2009}, volume={22}, pages={1609-1615} }

## Figures from this paper

## 45 Citations

### Perfect state transfer, integral circulants, and join of graphs

- MathematicsQuantum Inf. Comput.
- 2010

It is shown that the integral circulant ICGn (2, n/2b) has perfect state transfer, where b ∈ {1, 2},n is a multiple of 16 and Q is a subset of the odd divisors of n.

### Further results on the perfect state transfer in integral circulant graphs

- MathematicsComput. Math. Appl.
- 2011

### Characterization of quantum circulant networks having perfect state transfer

- MathematicsQuantum Inf. Process.
- 2013

This paper answers the question of when circulant quantum spin networks with nearest-neighbor couplings can give perfect state transfer and calculates perfect quantum communication distance (distance between vertices where PST occurs) and describes the spectra of integralcirculant graphs having PST.

### Perfect state transfer on Cayley graphs over dihedral groups

- MathematicsLinear and Multilinear Algebra
- 2019

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

### On quantum perfect state transfer in weighted join graphs

- Mathematics
- 2009

We study perfect state transfer on quantum networks represented by weighted graphs. Our focus is on graphs constructed from the join and related graph operators. Some specific results we prove…

### Quantum state transfer on integral oriented circulant graphs

- Mathematics
- 2022

An oriented circulant graph is called integral if all eigenvalues of its Hermitian adjacency matrix are integers. The main purpose of this paper is to investigate the existence of perfect state…

### Perfect state transfer on bi-Cayley graphs over abelian groups

- Mathematics
- 2022

The study of perfect state transfer on graphs has attracted a great deal of attention during the past ten years because of its applications to quantum information processing and quantum computation.…

## References

SHOWING 1-10 OF 13 REFERENCES

### Longest Induced Cycles in Circulant Graphs

- MathematicsElectron. J. Comb.
- 2005

Using residues modulo the primes dividing $n$, a representation of the vertices is introduced that reduces the problem to a purely combinatorial question of comparing strings of symbols and proves that the multiplicity of each prime dividing n has no effect on the length of the longest induced cycle in X_n.

### Sequentially Perfect and Uniform One-Factorizations of the Complete Graph

- Mathematics, Computer ScienceElectron. J. Comb.
- 2005

This paper proposes a weakening of the definitions of uniform and perfect one-factorizations of the complete graph in such a way that the union of any two (cyclically) consecutive one-factors is always isomorphic to the same two-regular graph.

### Perfect state transfer in quantum spin networks.

- PhysicsPhysical review letters
- 2004

It is shown that 2log3N is the maximal perfect communication distance for hypercube geometries if one allows fixed but different couplings between the qubits, then perfect state transfer can be achieved over arbitrarily long distances in a linear chain.

### Which graphs have integral spectra

- Mathematics
- 1974

The spectrum S(G) of a graph G of order p is defined as the non-increasing sequence of the p real eigenvalues of the adjacency matrix of G. It has been found that certain graphs have an integral…

### Parameters of Integral Circulant Graphs and Periodic Quantum Dynamics

- Engineering
- 2007

The means for simultaneous scouring of metal surfaces contains a waste product in manufacture of fodder yeast, citric acid, ammonium citrate, aqueous solution of sodium gluconate, sulphonated ricinic…

### An Introduction to the Theory of Numbers

- Philosophy
- 1938

This is the fifth edition of a work (first published in 1938) which has become the standard introduction to the subject. The book has grown out of lectures delivered by the authors at Oxford,…