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arXiv · 1609.00420

Note on von Neumann and Rényi entropies of a Graph

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 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.

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Michael Dairyko, Leslie Hogben, Jephian C. -H. Lin, Joshua Lockhart, David Roberson, Simone Severini, Michael Young. 2016-09-01. Note on von Neumann and Rényi entropies of a Graph. https://arxiv.org/abs/1609.00420

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