Paper Info
Title
On graphs whose Laplacian matrix's multipartite separability is invariant under graph isomorphism
Abstract
Normalized Laplacian matrices of graphs have recently been studied in the context of quantum mechanics as density matrices of quantum systems. Of particular interest is the relationship between quantum physical properties of the density matrix and the graph theoretical properties of the underlying graph. One important aspect of density matrices is their entanglement properties, which are responsible for many nonintuitive physical phenomena. The entanglement property of normalized Laplacian matrices is in general not invariant under graph isomorphism. In recent papers, graphs were identified whose entanglement and separability properties are invariant under isomorphism. The purpose of this note is to completely characterize the set of graphs whose separability is invariant under graph isomorphism. In particular, we show that this set consists of K\"2\",\"2 and its complement, all complete graphs and no other graphs.
Year
DOI
Venue
2010
10.1016/j.disc.2010.06.014
Discrete Mathematics
Keywords
Field
DocType
laplacian matrix,graph isomorphism,entanglement,density matrix,quantum mechanics,complete graph,quantum physics
Graph automorphism,Laplacian matrix,Discrete mathematics,Combinatorics,Graph property,Graph isomorphism,Graph homomorphism,Multipartite graph,Cograph,Graph product,Mathematics
Journal
Volume
Issue
ISSN
310
21
Discrete Mathematics
Citations 
PageRank 
References 
3
0.55
3
Authors
1
Name
Order
Citations
PageRank
Chai Wah Wu133067.62