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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

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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:
DateEvent
1 June 2018Published
9 February 2018Available
7 February 2018Accepted
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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