# Quantum graph walks II: Quantum walks on graph coverings

@article{Higuchi2012QuantumGW, title={Quantum graph walks II: Quantum walks on graph coverings}, author={Yusuke Higuchi and Norio Konno and Iwao Sato and Etsuo Segawa}, journal={arXiv: Mathematical Physics}, year={2012} }

We give a new determinant expression for the characteristic polynomial of the bond scattering matrix of a quantum graph G. Also, we give a decomposition formula for the characteristic polynomial of the bond scattering matrix of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express the characteristic polynomial of the bond scattering matrix of a regular covering of G by means of its L-functions. As an application… CONTINUE READING

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