On eigenvalues and the energy of dendrimer trees

Hengmeng Xu and Weigen Yan

Applied Mathematics and Computation, 2022, vol. 424, issue C

Abstract: A dendrimer tree Dn,k is a rooted tree with root v0 in which the root vertex v0 has k children, the vertices u satisfying the distance d(v0,u)=i have k−1 children for 1≤i≤n−1, and the vertices u such that d(v0,u)=n are pendant vertices. In this paper, we obtain almost all of eigenvalues of Dn,k except n+1 eigenvalues which are just the roots of the matching polynomial of a weighted path with n+1 vertices v0,v1,…,vn and n edges (v0,v1),(v1,v2),(v2,v3)⋯,(vn−1,vn), of weights equal to k,k−1,k−1,⋯,k−1, and we obtain a formula to compute the energy of Dn,k.

Keywords: Bethe tree; Dendrimer tree; Characteristic polynomial; Matching polynomial; Energy (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:424:y:2022:i:c:s0096300322001370

DOI: 10.1016/j.amc.2022.127051

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