Perfect state transfer in unitary Cayley graphs over local rings

Document Type: Research Paper

Authors

Chulalongkorn University

Abstract

‎In this work‎, ‎using eigenvalues and eigenvectors of unitary Cayley graphs over finite local rings and elementary linear algebra‎, ‎we characterize which local rings allowing PST occurring in its unitary Cayley graph‎. ‎Moreover‎, ‎we have some developments when $R$ is a product of local rings‎.

Keywords

Main Subjects


R. Akhtar, M. Boggess, T. Jackson-Henderson, I. Jimenez, R. Karpman, A. Kinzel and D. Pritikin (2009). On the unitary Cayley graph of a finite ring. Electron. J. Combin.. 16, 13
R. J. Angeles-Canul, R. Norton, M. Opperman, C. Paribello, M. Russell and C. Tamon (2010). Perfect state transfer, integral circulants and join of graphs. Quantum Inf. Comput.. 10 (3-4), 325-342
M. Basic, M. D. Petkovic and D. Stevanovic (2009). Perfect state transfer in integral circulant graphs. Appl. Math. Lett.. 22, 1117-1121
W.-C. Cheung and C. Godsil (2011). Perfect state transfer in cubelike graphs. Linear Al gebra Appl.. 435, 2468-2474
S. H. Friedberg, A. J. Insel and L. E. Spence (2003). Linear Algebra. 4th edn, Prentice Hall, New Jersey.
N. Ganesan (1964). Properties of rings with a nite number of zero divisors. Math. Ann.. 157, 215-218
Y. Ge, B. Greenberg, O. Perez and C. Tamon (2011). Perfect state transfer, graph products and equitable partitions,. Int. J. Quantum Inf.. 9, 823-842
C. Godsil (2012). State transfer on graphs. Discrete Math.. 312, 129-147
J. Kempe (2003). Quantum random walks-an introductory overview. Contemporary Physics. 44, 307-327
V. Kendon (2006). Quantum walks on general graphs. Int. J. Quantum Inform.. 4 (3), 791-805
D. Kiani, M. M. H. Aghaei, Y. Meemark and B. Suntornpoch (2011). Energy of unitary Cayley graphs and gcd-graphs. Linear Algebra Appl.. 435, 1336-1343
D. Singmaster and D. M. Bloom (1964). Problems and Solutions: Solutions of Elementary Problems: E1648. Amer. Math. Monthly. 71, 918-920