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Parameters of integral circulant graphs and periodic quantum dynamics

Saxena, N; Severini, S; Shparlinski, IE; (2007) Parameters of integral circulant graphs and periodic quantum dynamics. INT J QUANTUM INF , 5 (3) 417 - 430.

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Abstract

The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system whose hamiltonian is identical to the adjacency matrix of a circulant graph is periodic if and only if all eigenvalues of the graph are integers (that is, the graph is integral). Motivated by this observation, we focus on relevant properties of integral circulant graphs. Specifically, we bound the number of vertices of integral circulant graphs in terms of their degree, characterize bipartiteness and give exact bounds for their diameter. Additionally, we prove that circulant graphs with odd order do not allow perfect state transfer.

Type:Article
Title:Parameters of integral circulant graphs and periodic quantum dynamics
Keywords:circulant graphs, integral graphs, periodic dynamics, perfect state transfer
UCL classification:UCL > School of BEAMS > Faculty of Engineering Science > Computer Science

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