1. State transfer and star complements in graphs.
- Author
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Jiang Zhou and Changjiang Bu
- Subjects
- *
GRAPH theory , *EIGENVALUES , *MULTIPLICITY (Mathematics) , *OPERATOR theory , *MATRIX groups , *MATHEMATICAL analysis - Abstract
Let G be a graph with adjacency matrix A, and let H(t)=exp(itA). For an eigenvalue μ of A with multiplicity k, a star set for μ in G is a vertex set X of G such that |X|=k and the induced subgraph G-X does not have μ as an eigenvalue. G is said to have perfect state transfer from the vertex u to the vertex v if there is a time τ such that |H(τ)u,v|=1. The unitary operator H(t) has important applications in the transfer of quantum information. In this paper, we give an expression of H(t). For a star set X of graph G, perfect state transfer does not occur between any two vertices in X. We also give some results for the existence of perfect state transfer in a graph. [ABSTRACT FROM AUTHOR]
- Published
- 2014
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