Journal or Book Title
Linear Algebra and Its Applications
We conjecture that all connected graphs of order n have von Neumann entropy at least as great as the star K1;n1 and prove this for almost all graphs of order n. We show that connected graphs of order n have Renyi 2-entropy at least as great as K1;n1 and for > 1, Kn maximizes Renyi -entropy over graphs of order n. We show that adding an edge to a graph can lower its von Neumann entropy.
This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
Dairyko, Michael; Hogben, Leslie; Lin, Jephian C.H.; Lockhart, Joshua; Roberson, David; Severini, Simone; and Young, Michael, "Note on von Neumann and Rényi Entropies of a Graph" (2017). Mathematics Publications. 63.