Parameters of Integral circulant graphs and periodic quantum dynamics | Macquarie University ResearchOnline

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Title: Parameters of Integral circulant graphs and periodic quantum dynamics
Related: International journal of quantum information, Vol. 5, Issue 3, p.417-430
DOI: 10.1142/S0219749907002918
Publisher: World Scientific Publishing
Date: 2007
Author/Creator: Saxena, Nitin
Author/Creator: Severini, Simone
Author/Creator: Shparlinski, Igor E
Description: 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.
Description: 14 page(s)
Subject Keyword: circulant graphs
Subject Keyword: integral graphs
Subject Keyword: periodic dynamics
Subject Keyword: perfect state transfer
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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