1. Note on von Neumann and Rényi entropies of a graph.
- Author
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Dairyko, Michael, Hogben, Leslie, Lin, Jephian C.-H., Lockhart, Joshua, Roberson, David, Severini, Simone, and Young, Michael
- Subjects
- *
VON Neumann algebras , *RENYI'S entropy , *GRAPH theory , *TOPOLOGY , *COMBINATORICS - Abstract
We conjecture that all connected graphs of order n have von Neumann entropy at least as great as the star K 1 , n − 1 and prove this for almost all graphs of order n . We show that connected graphs of order n have Rényi 2-entropy at least as great as K 1 , n − 1 and for α > 1 , K n maximizes Rényi α -entropy over graphs of order n . We show that adding an edge to a graph can lower its von Neumann entropy. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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