Related papers: The discrete-time Grover walk on star graphs with …

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This paper has been withdrawn, as it has been merged into arXiv:1009.6144

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We propose a phenomenon of discrete-time quantum walks on graphs called the pulsation, which is a generalization of a phenomenon in the quantum searches. This phenomenon is discussed on a composite graph formed by two connected graphs…

This paper has been withdrawn by the author due to a crucial error.

The paper has been withdrawn due to a crucial error in section 3.

This paper has been withdrawn by the author, since some results of the paper have been already obtained in [J.~Lewandowski, Class. Quantum Grav. 9 (1992), no. 10, L147--L151.]

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This paper has been withdrawn while the author verifies the literature.

This paper has been withdrawn by the author. Proofs of two propositions need more details.

This paper has been withdrawn by the author.The formula which was proposed gives only a second order deformation.

This paper has been withdrawn by the author due to the paper does not belong to Condensed Matter field.

This paper is being withdrawn.