Note on von Neumann and R\'enyi entropies of a Graph

Michael Dairyko; Leslie Hogben; Jephian C. -H. Lin; Joshua Lockhart; David Roberson; Simone Severini; Michael Young

Note on von Neumann and R\'enyi entropies of a Graph

Combinatorics 2016-09-05 v1 Quantum Physics

Authors: Michael Dairyko , Leslie Hogben , Jephian C. -H. Lin , Joshua Lockhart , David Roberson , Simone Severini , Michael Young

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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 R\'enyi 2-entropy at least as great as $K_{1,n-1}$ and for $\alpha>1$ , $K_n$ maximizes R\'enyi $\alpha$ -entropy over graphs of order $n$ . We show that adding an edge to a graph can lower its von Neumann entropy.

Keywords

von Neumann entropy Renyi entropy connected graph star graph graph theory

Cite

@article{arxiv.1609.00420,
  title  = {Note on von Neumann and R\'enyi entropies of a Graph},
  author = {Michael Dairyko and Leslie Hogben and Jephian C. -H. Lin and Joshua Lockhart and David Roberson and Simone Severini and Michael Young},
  journal= {arXiv preprint arXiv:1609.00420},
  year   = {2016}
}

Note on von Neumann and R\'enyi entropies of a Graph

Abstract

Keywords

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