On majorization of closed walk vectors of trees with given degree sequences

Ya-Hong Chen, Daniel Gray, Ya-Lei Jin and Xiao-Dong Zhang

Applied Mathematics and Computation, 2018, vol. 336, issue C, 326-337

Abstract: Let Cv(k; T) be the number of closed walks of length k starting at vertex v in a tree T. We prove that for any tree T with a given degree sequence π, the vector C(k; T) ≡ (Cv(k; T), v ∈ V(T)) is weakly majorized by the vector C(k;Tπ*)≡(Cv(k;Tπ*),v∈V(Tπ*)), where Tπ* is the greedy tree with the degree sequence π. In addition, for two trees degree sequences π and π′, if π is majorized by π′, then C(k;Tπ*) is weakly majorized by C(k;Tπ′*).

Keywords: Majorization; Closed walk; Trees; Degree sequence (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:336:y:2018:i:c:p:326-337

DOI: 10.1016/j.amc.2018.05.007

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