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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 ISSN 0024-3795.
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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 | ||||||||
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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 | ||||||||
Date of first compliant deposit: | 8 February 2018 | ||||||||
Date of first compliant Open Access: | 13 February 2018 |
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