Perfect state transfer in integral circulant graphs of non-square-free order

@article{Basic2010PerfectST,
  title={Perfect state transfer in integral circulant graphs of non-square-free order},
  author={Milan Basic and Marko D. Petkovi{\'c}},
  journal={Linear Algebra and its Applications},
  year={2010},
  volume={433},
  pages={149-163}
}

The maximal energy of classes of integral circulant graphs

Perfect state transfer on abelian Cayley graphs

Perfect state transfer in NEPS of some graphs

ABSTRACT Let G be a graph with adjacency matrix . The transition matrix of G corresponding to is denoted as . If there is some time such that has unit modulus, where u and v are distinct vertices in

Perfect state transfer in unitary Cayley graphs and gcd-graphs

Abstract In this work, we consider the problem on the existence of perfect state transfer in unitary Cayley graphs and gcd-graphs over finite commutative rings. We characterize all finite commutative

State transfer and star complements in graphs

Perfect State Transfer in Quantum Walks on Graphs

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 ingredient of

The exact maximal energy of integral circulant graphs with prime power order

All divisor sets maximising the energy of an integral circulant graph of order $p^s$ are determined, which enables us to compute the maximal energy $\Emax{ p^s}$ among all integralcirculant graphs of order p.s.

State transfer on graphs

Counting subgraphs of regular graphs using spectral moments

This thesis introduces a novel approach to counting subgraphs of regular graphs. This is useful for relating the algebraic properties of a graph G to its structural properties; namely the eigenvalues

References

SHOWING 1-10 OF 20 REFERENCES

On the clique number of integral circulant graphs

Sequentially Perfect and Uniform One-Factorizations of the Complete Graph

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.

Longest Induced Cycles in Circulant Graphs

  • E. Fuchs
  • Mathematics
    Electron. 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.

Periodic Graphs

It is shown that, for a class of graphs X including all vertex-transitive graphs, if perfect state transfer occurs at time τ , then H(τ) is a scalar multiple of a permutation matrix of order two with no fixed points.

Which graphs have integral spectra

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

Integral circulant graphs

Graphs with integral spectrum