Note on von Neumann and Renyi entropies of a graph

作者：Dairyko, Michael; Hogben, Leslie; Lin, Jephian. C. H.^*; Lockhart, Joshua; Roberson, David; Severini, Simone; Young, Michael

来源：Linear Algebra and Its Applications, 2017, 521: 240-253.

DOI：10.1016/j.laa.2017.01.037

• Entropy
• Quantum
• Laplacian
• Graph
• Matrix

We conjecture that all connected graphs of order n have von Neumann entropy at least as great as the star K-1,K-n-1 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 K-1,K-n-1 and for alpha > 1, K-n maximizes Renyi alpha-entropy over graphs of order n. We show that adding an edge to a graph can lower its von Neumann entropy.

• 出版日期2017-5-15
• 单位上海交通大学