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

2016

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

Dairyko, Michael, Hogben, Leslie, Lin, Jephian C. -H. et al.

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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.

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