首页|On eigenvalues and the energy of dendrimer trees
On eigenvalues and the energy of dendrimer trees
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NSTL
Elsevier
A dendrimer tree D-n,D-k is a rooted tree with root v(0) in which the root vertex v(0) has k children, the vertices u satisfying the distance d(v(0), u) = i have k - 1 children for 1 <= i <= n - 1, and the vertices u such that d(v(0) , u) = n are pendant vertices. In this paper, we obtain almost all of eigenvalues of D-n,D-k except n + 1 eigenvalues which are just the roots of the matching polynomial of a weighted path with n + 1 vertices v(0), v(1), ..., v(n) and n edges (v(0), v(1)), (v(1), v(2)), (v(2), v(3)) ..., (v(n-1), v(n)), of weights equal to k, k - 1, k - 1, ..., k - 1, and we obtain a formula to compute the energy of D-n,D-k. (C) 2022 Elsevier Inc. All rights reserved.
NSTL
Elsevier
