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State transfer and star complements in graphs.
- Source :
-
Discrete Applied Mathematics . Oct2014, Vol. 176, p130-134. 5p. - Publication Year :
- 2014
-
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]
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 176
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 97418971
- Full Text :
- https://doi.org/10.1016/j.dam.2013.08.028