Note on von Neumann and Rényi Entropies of a Graph
Date
2017-05-15
Authors
Dairyko, Michael
Lin, Jephian
Lockhart, Joshua
Roberson, David
Severini, Simone
Young, Michael
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Series Number
Journal Issue
Is Version Of
Versions
Series
Academic or Administrative Unit
Type
article
Comments
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.
Rights Statement
Copyright
Sun Jan 01 00:00:00 UTC 2017