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\iteman{io-port 05960027}
\itemau{Godsil, Chris; Guo, Krystal}
\itemti{Quantum walks on regular graphs and eigenvalues.}
\itemso{Electron. J. Comb. 18, No. 1, Research Paper P165, 9 p., electronic only (2011).}
\itemab
Summary: We study the transition matrix of a quantum walk on strongly regular graphs. It is proposed by {\it D. Emms}, {\it E. R. Hancock}, {\it S. Severini} and {\it R. C. Wilson} [Electron. J. Comb. 13, No. 1, Research paper R34, 14 p. (2006; Zbl 1099.05082)], that the spectrum of $S^+(U^3)$, a matrix based on the amplitudes of walks in the quantum walk, distinguishes strongly regular graphs. We find the eigenvalues of $S^+(U )$ and $S^+(U^2)$ for regular graphs and show that $S^+(U^2) = S^+(U )^2 + I$.
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\itemut{transition matrix; quantum walk; strongly regular graphs; spectrum; eigenvalues}
\itemli{emis:journals/EJC/Volume\_18/Abstracts/v18i1p165.html}
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