Spectral properties of balanced trees and dendrimers

TL;DR

This paper analyzes the spectral properties of balanced trees and dendrimers, deriving formulas for their characteristic polynomials, spectra, and energy bounds to unify and enhance existing results in graph spectral theory.

Contribution

It introduces a semi-factorized formula for characteristic polynomials and provides new bounds for the energy of dendrimers, advancing spectral analysis methods.

Findings

Derived semi-factorized characteristic polynomial formulas.

Determined spectra of balanced trees and dendrimers.

Provided bounds for dendrimer energy.

Abstract

We investigate the spectral properties of balanced trees and dendrimers, with a view toward unifying and improving the existing results. Here we find a semi-factorized formula for their characteristic polynomials. Afterwards, we determine their spectra via the aforementioned factors. In the end, we analyze the behavior of the energy of dendrimers and compute lower and upper bound approximations for it.