Dairyko, M;
Hogben, L;
Lin, JCH;
Lockhart, J;
Roberson, D;
Severini, S;
Young, M;
(2017)
Note on von Neumann and Renyi entropies of a graph.
Linear Algebra and its Applications
, 521
pp. 240-253.
10.1016/j.laa.2017.01.037.
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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,n−1 and prove this for almost all graphs of order n. We show that connected graphs of order n have R´enyi 2-entropy at least as great as K1,n−1 and for α > 1, Kn maximizes R´enyi α-entropy over graphs of order n. We show that adding an edge to a graph can lower its von Neumann entropy.
| Type: | Article |
|---|---|
| Title: | Note on von Neumann and Renyi entropies of a graph |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.laa.2017.01.037 |
| Publisher version: | http://doi.org/10.1016/j.laa.2017.01.037 |
| Language: | English |
| Additional information: | © 2017 Elsevier Inc. All rights reserved. This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Entropy, Quantum, Laplacian, Graph, Matrix |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1526412 |
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