Note on von Neumann and Rényi Entropies of a Graph
Date
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Authors
Research Projects
Organizational Units
The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.
History
The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.
Dates of Existence
1909-present
Historical Names
- Department of Electrical Engineering (1909-1985)
- Department of Electrical Engineering and Computer Engineering (1985-1995)
Related Units
- College of Engineering (parent college)
- Department of Physics and Electrical Engineering (predecessor)
Journal Issue
Is Version Of
Versions
Series
Department
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.
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.