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Walk entropy and walk-regularity
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Kloster, Kyle, Králʼ, Daniel and Sullivan, Blair D. (2018) Walk entropy and walk-regularity. Linear Algebra and Its Applications, 546 . pp. 115-121. doi:10.1016/j.laa.2018.02.009
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WRAP-walk-entropy-walk-regulartity-Kral-2018.pdf - Accepted Version - Requires a PDF viewer. Download (455Kb) | Preview |
Official URL: https://doi.org/10.1016/j.laa.2018.02.009
Abstract
A graph is said to be walk-regular if, for each ℓ≥1, every vertex is contained in the same number of closed walks of length ℓ. We construct a 24-vertex graph H4 that is not walk-regular yet has maximized walk entropy, SV(H4,β)=log24, for some β>0. This graph is a counterexample to a conjecture of Benzi [Linear Algebra Appl.~443 (2014), 395--399, Conjecture 3.1]. We also show that there exist infinitely many temperatures β0>0 so that SV(G,β0)=lognG if and only if a graph G is walk-regular.
| Item Type: | Journal Article | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
| Library of Congress Subject Headings (LCSH): | Graph theory, Entropy, Algebras, Linear | ||||||||
| Journal or Publication Title: | Linear Algebra and Its Applications | ||||||||
| Publisher: | Elsevier Inc | ||||||||
| ISSN: | 0024-3795 | ||||||||
| Official Date: | 1 June 2018 | ||||||||
| Dates: |
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| Volume: | 546 | ||||||||
| Page Range: | pp. 115-121 | ||||||||
| DOI: | 10.1016/j.laa.2018.02.009 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access |
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