Note on von Neumann and Rényi Entropies of a Graph

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2017-05-15
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Dairyko, Michael
Hogben, Leslie
Lin, Jephian
Lockhart, Joshua
Roberson, David
Severini, Simone
Young, Michael
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Hogben, Leslie
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Mathematics
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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 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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This is a manuscript of an article published as Dairyko, Michael, Leslie Hogben, Jephian C-H. Lin, Joshua Lockhart, David Roberson, Simone Severini, and Michael Young. "Note on von Neumann and Rényi entropies of a graph." Linear Algebra and its Applications 521 (2017): 240-253. DOI: 10.1016/j.laa.2017.01.037. Posted with permission.

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Sun Jan 01 00:00:00 UTC 2017
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