Mathematics, Electrical and Computer Engineering
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.
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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.